calculating direction of the player to shoot pygame

The unit of the angle for the mathematical operations math.sin and math.cos is radian, but the unit of the angel for pygame.transform.rotate() is degrees. Furthermore you have to create a pygame.Surface with the flag SRCALPHA and to fill the surface with the bullet color, before it is rotated:

class Bullet:
    def __init__(self):
        self.pos = [player1.pos[0], player1.pos[1]]
        self.direction = math.radians(player1.rotation_angle)
        self.bullet = pygame.Surface((10, 5), pygame.SRCALPHA)
        self.bullet.fill((100, 200, 120))
        self.rotated_bullet = pygame.transform.rotate(self.bullet, player1.rotation_angle)
        self.time = 0

In pygame the y axis points form the top to the bottom. That is the opposite direction than in a usual Cartesian coordinate system. Because of that the y coordinate of the direction has to be inverted:

class Bullet:
    # [...]

    def shoot(self):
        self.pos[0] += math.cos(self.direction) * self.time
        self.pos[1] -= math.sin(self.direction) * self.time
        self.time += 0.5

See the example:

import pygame
import math

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

class Player():
    def  __init__(self):
        self.rotation_angle = 0
        self.player = pygame.Surface((20, 20), pygame.SRCALPHA)
        self.player.fill((0, 255, 0))
        self.rotated_player = self.player
        self.pos = (WIDTH//2, HEIGHT//2)
        
    def rotate(self, keys, left, right):
        if keys[right]:
            self.rotation_angle -= 0.5
        if keys[left]:
            self.rotation_angle += 0.5
        self.rotated_player = pygame.transform.rotate(self.player, (self.rotation_angle))

class Bullet:
    def __init__(self):
        self.pos = [player1.pos[0], player1.pos[1]]
        self.direction = math.radians(player1.rotation_angle)
        self.bullet = pygame.Surface((10, 5), pygame.SRCALPHA)
        self.bullet.fill((100, 200, 120))
        self.rotated_bullet = pygame.transform.rotate(self.bullet, player1.rotation_angle)
        self.time = 0

    def shoot(self):
        self.pos[0] += math.cos(self.direction) * self.time
        self.pos[1] -= math.sin(self.direction) * self.time
        self.time += 0.5

player1 = Player()

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.KEYDOWN and event.key == pygame.K_SPACE:
            bullets.append(Bullet())

    keys = pygame.key.get_pressed()
    player1.rotate(keys, pygame.K_LEFT, pygame.K_RIGHT)       

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

    window.fill(0)
    window.blit(player1.rotated_player, player1.rotated_player.get_rect(center=player1.pos))
    for bullet in bullets:
        window.blit(bullet.rotated_bullet, bullet.rotated_bullet.get_rect(center=bullet.pos))
    pygame.display.flip()

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_{See also}

Why aren’t any bullets appearing on screen? – pygame
Shooting a bullet in pygame in the direction of mouse