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()