Shooting a bullet in pygame in the direction of mouse

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First of all pygame.transform.rotate does not transform the object itself, but creates a new rotated surface and returns it.

If you want to fire a bullet in a certain direction, the direction is defined the moment the bullet is fired, but it does not change continuously.
When the bullet is fired, set the starting position of the bullet and calculate the direction vector to the mouse position:

self.pos = (x, y)
mx, my = pygame.mouse.get_pos()
self.dir = (mx - x, my - y)

The direction vector should not depend on the distance to the mouse, but it has to be a Unit vector.
Normalize the vector by dividing by the Euclidean distance

length = math.hypot(*self.dir)
if length == 0.0:
    self.dir = (0, -1)
else:
    self.dir = (self.dir[0]/length, self.dir[1]/length)

Compute the angle of the vector and rotate the bullet. In general, the angle of a vector can be computed by atan2(y, x). The y-axis needs to be reversed (atan2(-y, x)) as the y-axis generally points up, but in the PyGame coordinate system the y-axis points down (see How to know the angle between two points?):

angle = math.degrees(math.atan2(-self.dir[1], self.dir[0]))

self.bullet = pygame.Surface((7, 2)).convert_alpha()
self.bullet.fill((255, 255, 255))
self.bullet = pygame.transform.rotate(self.bullet, angle)

To update the position of the bullet, it is sufficient to scale the direction (by a velocity) and add it to the position of the bullet:

self.pos = (self.pos[0]+self.dir[0]*self.speed, 
            self.pos[1]+self.dir[1]*self.speed)

To draw the rotated bullet in the correct position, take the bounding rectangle of the rotated bullet and set the center point with self.pos (see How do I rotate an image around its center using PyGame?):

bullet_rect = self.bullet.get_rect(center = self.pos)
surf.blit(self.bullet, bullet_rect)

See also Shoot bullets towards target or mouse

Minimal example: repl.it/@Rabbid76/PyGame-FireBulletInDirectionOfMouse

import pygame
import math

pygame.init()
window = pygame.display.set_mode((500, 500))
clock = pygame.time.Clock()

class Bullet:
    def __init__(self, x, y):
        self.pos = (x, y)
        mx, my = pygame.mouse.get_pos()
        self.dir = (mx - x, my - y)
        length = math.hypot(*self.dir)
        if length == 0.0:
            self.dir = (0, -1)
        else:
            self.dir = (self.dir[0]/length, self.dir[1]/length)
        angle = math.degrees(math.atan2(-self.dir[1], self.dir[0]))

        self.bullet = pygame.Surface((7, 2)).convert_alpha()
        self.bullet.fill((255, 255, 255))
        self.bullet = pygame.transform.rotate(self.bullet, angle)
        self.speed = 2

    def update(self):  
        self.pos = (self.pos[0]+self.dir[0]*self.speed, 
                    self.pos[1]+self.dir[1]*self.speed)

    def draw(self, surf):
        bullet_rect = self.bullet.get_rect(center = self.pos)
        surf.blit(self.bullet, bullet_rect)  

bullets = []
pos = (250, 250)
run = True
while run:
    clock.tick(60)
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False
        if event.type == pygame.MOUSEBUTTONDOWN:
            bullets.append(Bullet(*pos))

    for bullet in bullets[:]:
        bullet.update()
        if not window.get_rect().collidepoint(bullet.pos):
            bullets.remove(bullet)

    window.fill(0)
    pygame.draw.circle(window, (0, 255, 0), pos, 10)
    for bullet in bullets:
        bullet.draw(window)
    pygame.display.flip()

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