bullet.setX(bullet.getX() + stepSizePerFrame * Math.cos(Math.toRadians(bullet.getAngle())));
bullet.setY(bullet.getY() + stepSizePerFrame * Math.sin(Math.toRadians(bullet.getAngle())));
This shows you how can you can move a bullet with a fixed angle. Same for your character, you just need a dynamic angle, you can change the angle of the character by rotating him (for example let him look at the mouse pointer) then just calculate the angle. For the angle of a bullet you can take the angle of the character, when you press the shoot button.