The inaccuracy will be due to accumulated rounding error. There will be a small amount of rounding error in your bullet's x and y velocities because we don't have infinite precision. Let's say there is an error of 0.1 pixels in the x speed. If you add that speed to a position 100 times, then the error will have grown to 100 * 0.1 = 10 pixels.

I think you have two options. You could just keep recalculating the speed every step. That will get rid of accumulated error.

Or you try to reduce the error at the begining. I suspect that the trigonometric functions are introducing some error for reasons I won't get into here. I would try using unit vectors instead.

(This code is based on some earlier code that you deleted.)

    def getUnitVector(x1, y1, x2, y2):
        delx = x2 - x1
        dely = y2 - y1
        m = math.sqrt(delx * delx + dely * dely)
        unit = (delx / m, dely / m)
        return unit

    aim = getUnitVector(startx, starty, mousex, mousey)

    bx = BULLETSPEED * aim[0]
    by = BULLETSPEED * aim[1]