In PyGame, collision detection is done using pygame.Rect objects. The Rect object offers various methods for detecting collisions between objects. Even the collision between a rectangular and circular object such as a paddle and a ball can be detected by a collision between two rectangular objects, the paddle and the bounding rectangle of the ball.

Some examples:

• pygame.Rect.collidepoint:

  Test if a point is inside a rectangle

  repl.it/@Rabbid76/PyGame-collidepoint

  import pygame
  
  pygame.init()
  window = pygame.display.set_mode((250, 250))
  rect = pygame.Rect(*window.get_rect().center, 0, 0).inflate(100, 100)
  
  run = True
  while run:
      for event in pygame.event.get():
          if event.type == pygame.QUIT:
              run = False
  
      point = pygame.mouse.get_pos()
      collide = rect.collidepoint(point)
      color = (255, 0, 0) if collide else (255, 255, 255)
  
      window.fill(0)
      pygame.draw.rect(window, color, rect)
      pygame.display.flip()
  
  pygame.quit()
  exit()
  

• pygame.Rect.colliderect

  Test if two rectangles overlap

  See also How to detect collisions between two rectangular objects or images in pygame

  repl.it/@Rabbid76/PyGame-colliderect

  import pygame
  
  pygame.init()
  window = pygame.display.set_mode((250, 250))
  rect1 = pygame.Rect(*window.get_rect().center, 0, 0).inflate(75, 75)
  rect2 = pygame.Rect(0, 0, 75, 75)
  
  run = True
  while run:
      for event in pygame.event.get():
          if event.type == pygame.QUIT:
              run = False
  
      rect2.center = pygame.mouse.get_pos()
      collide = rect1.colliderect(rect2)
      color = (255, 0, 0) if collide else (255, 255, 255)
  
      window.fill(0)
      pygame.draw.rect(window, color, rect1)
      pygame.draw.rect(window, (0, 255, 0), rect2, 6, 1)
      pygame.display.flip()
  
  pygame.quit()
  exit()
  

Furthermore, pygame.Rect.collidelist and pygame.Rect.collidelistall can be used for the collision test between a rectangle and a list of rectangles. pygame.Rect.collidedict and pygame.Rect.collidedictall can be used for the collision test between a rectangle and a dictionary of rectangles.

The collision of pygame.sprite.Sprite and pygame.sprite.Group objects, can be detected by pygame.sprite.spritecollide(), pygame.sprite.groupcollide() or pygame.sprite.spritecollideany(). When using these methods, the collision detection algorithm can be specified by the collided argument:

The collided argument is a callback function used to calculate if two sprites are colliding.

Possible collided callables are collide_rect, collide_rect_ratio, collide_circle, collide_circle_ratio, collide_mask

Some examples:

• pygame.sprite.spritecollide()

  repl.it/@Rabbid76/PyGame-spritecollide

  import pygame
  
  pygame.init()
  window = pygame.display.set_mode((250, 250))
  
  sprite1 = pygame.sprite.Sprite()
  sprite1.image = pygame.Surface((75, 75))
  sprite1.image.fill((255, 0, 0))
  sprite1.rect = pygame.Rect(*window.get_rect().center, 0, 0).inflate(75, 75)
  sprite2 = pygame.sprite.Sprite()
  sprite2.image = pygame.Surface((75, 75))
  sprite2.image.fill((0, 255, 0))
  sprite2.rect = pygame.Rect(*window.get_rect().center, 0, 0).inflate(75, 75)
  
  all_group = pygame.sprite.Group([sprite2, sprite1])
  test_group = pygame.sprite.Group(sprite2)
  
  run = True
  while run:
      for event in pygame.event.get():
          if event.type == pygame.QUIT:
              run = False
  
      sprite1.rect.center = pygame.mouse.get_pos()
      collide = pygame.sprite.spritecollide(sprite1, test_group, False)
  
      window.fill(0)
      all_group.draw(window)
      for s in collide:
          pygame.draw.rect(window, (255, 255, 255), s.rect, 5, 1)
      pygame.display.flip()
  
  pygame.quit()
  exit()
  

For a collision with masks, see How can I make a collision mask? or Pygame mask collision

See also Collision and Intersection

• pygame.sprite.spritecollide() / collide_circle

  repl.it/@Rabbid76/PyGame-spritecollidecollidecircle

  import pygame
  
  pygame.init()
  window = pygame.display.set_mode((250, 250))
  
  sprite1 = pygame.sprite.Sprite()
  sprite1.image = pygame.Surface((80, 80), pygame.SRCALPHA)
  pygame.draw.circle(sprite1.image, (255, 0, 0), (40, 40), 40)
  sprite1.rect = pygame.Rect(*window.get_rect().center, 0, 0).inflate(80, 80)
  sprite1.radius = 40
  sprite2 = pygame.sprite.Sprite()
  sprite2.image = pygame.Surface((80, 89), pygame.SRCALPHA)
  pygame.draw.circle(sprite2.image, (0, 255, 0), (40, 40), 40)
  sprite2.rect = pygame.Rect(*window.get_rect().center, 0, 0).inflate(80, 80)
  sprite2.radius = 40 
  
  all_group = pygame.sprite.Group([sprite2, sprite1])
  test_group = pygame.sprite.Group(sprite2)
  
  run = True
  while run:
      for event in pygame.event.get():
          if event.type == pygame.QUIT:
              run = False
  
      sprite1.rect.center = pygame.mouse.get_pos()
      collide = pygame.sprite.spritecollide(sprite1, test_group, False, pygame.sprite.collide_circle)
  
      window.fill(0)
      all_group.draw(window)
      for s in collide:
          pygame.draw.circle(window, (255, 255, 255), s.rect.center, s.rect.width // 2, 5)
      pygame.display.flip()
  
  pygame.quit()
  exit()
  

What does this all mean for your code?

pygame.Surface.get_rect.get_rect() returns a rectangle with the size of the Surface object, that always starts at (0, 0) since a Surface object has no position. The position of the rectangle can be specified by a keyword argument. For example, the centre of the rectangle can be specified with the keyword argument center. These keyword arguments are applied to the attributes of the pygame.Rect before it is returned (see pygame.Rect for a list of the keyword arguments).
See *Why is my collision test always returning ‘true’ and why is the position of the rectangle of the image always wrong (0, 0)?

You do not need the x and y attributes of Sprite and Bullet at all. Use the position of the rect attribute instead:

#Define the sprite class
class Sprite:
    def __init__(self, x, y, name):
        self.image = pygame.image.load(name)
        self.rect = self.image.get_rect(topleft = (x, y))

    def render(self):
        window.blit(self.image, self.rect)

# Define the bullet class to create bullets          
class Bullet:
    def __init__(self, x, y):
        self.bullet = pygame.image.load("user_bullet.BMP")
        self.rect = self.bullet.get_rect(topleft = (x + 23, y))

    def render(self):
        window.blit(self.bullet, self.rect)

Use pygame.Rect.colliderect() to detect collisions between instances of Sprite and Bullet.
See How to detect collisions between two rectangular objects or images in pygame:

my_sprite = Sprite(sx, sy, name)
my_bullet = Bullet(by, by)

while True:
    # [...]

    if my_sprite.rect.colliderect(my_bullet.rect):
        printe("hit")

From what I understand of pygame you just need to check if the two rectangles overlap using the colliderect method. One way to do it is to have a method in your Bullet class that checks for collisions:

def is_collided_with(self, sprite):
    return self.rect.colliderect(sprite.rect)

Then you can call it like:

sprite = Sprite(10, 10, 'my_sprite')
bullet = Bullet(20, 10)
if bullet.is_collided_with(sprite):
    print('collision!')
    bullet.kill()
    sprite.kill()

There is a very simple method for what you are trying to do using built in methods.

here is an example.

import pygame
import sys

class Sprite(pygame.sprite.Sprite):
    def __init__(self, pos):
        pygame.sprite.Sprite.__init__(self)
        self.image = pygame.Surface([20, 20])
        self.image.fill((255, 0, 0))
        self.rect = self.image.get_rect()

        self.rect.center = pos

def main():
    pygame.init()
    clock = pygame.time.Clock()
    fps = 50
    bg = [255, 255, 255]
    size =[200, 200]


    screen = pygame.display.set_mode(size)

    player = Sprite([40, 50])
    player.move = [pygame.K_LEFT, pygame.K_RIGHT, pygame.K_UP, pygame.K_DOWN]
    player.vx = 5
    player.vy = 5


    wall = Sprite([100, 60])

    wall_group = pygame.sprite.Group()
    wall_group.add(wall)

    player_group = pygame.sprite.Group()
    player_group.add(player)

    # I added loop for a better exit from the game
    loop = 1
    while loop:
        for event in pygame.event.get():
            if event.type == pygame.QUIT:
                loop = 0

        key = pygame.key.get_pressed()

        for i in range(2):
            if key[player.move[i]]:
                player.rect.x += player.vx * [-1, 1][i]

        for i in range(2):
            if key[player.move[2:4][i]]:
                player.rect.y += player.vy * [-1, 1][i]

        screen.fill(bg)

        # first parameter takes a single sprite
        # second parameter takes sprite groups
        # third parameter is a do kill command if true
        # all group objects colliding with the first parameter object will be
        # destroyed. The first parameter could be bullets and the second one
        # targets although the bullet is not destroyed but can be done with
        # simple trick bellow
        hit = pygame.sprite.spritecollide(player, wall_group, True)

        if hit:
            # if collision is detected call a function in your case destroy
            # bullet
            player.image.fill((255, 255, 255))

        player_group.draw(screen)
        wall_group.draw(screen)

        pygame.display.update()
        clock.tick(fps)

    pygame.quit()
    # sys.exit


if __name__ == '__main__':
    main()

Make a group for the bullets, and then add the bullets to the group.

What I would do is this:
In the class for the player:

def collideWithBullet(self):
    if pygame.sprite.spritecollideany(self, 'groupName'):
        print("CollideWithBullet!!")
        return True

And in the main loop somewhere:

def run(self):
    if self.player.collideWithBullet():
         print("Game Over")

Hopefully that works for you!!!

Inside the Sprite class, try adding a self.mask attribute with
self.mask = pygame.mask.from_surface(self.image)
and a collide_mask function inside of the Sprite class with this code:

    def collide_mask(self, mask):
        collided = False
        mask_outline = mask.outline()
        self.mask_outline = self.mask.outline()
        for point in range(len(mask_outline)):
            mask_outline[point] = list(mask_outline[point])
            mask_outline[point][0] += bullet.x
            mask_outline[point][1] += bullet.y
        for point in range(len(self.mask_outline)):
            self.mask_outline[point] = list(mask_outline[point])
            self.mask_outline[point][0] += self.x
            self.mask_outline[point][1] += self.y
        for point in mask_outline:
            for self_mask_point in self.mask_outline:
                if point = self_mask_point:
                    collided = True
        return collided