This is because you've mixed the Bullet and Platform behaviors together to manage the player's movement. If you're using Platform behavior then the player should not also be a bullet as well...
Try using an 'is_moving_right' boolean (or similar) and simulate the platform controls to make the player move in the same way - should work a treat!
Edit - I must be slow at typing! You can't mix the behaviors in the way you want so I'm afraid you'll have to change your idea (can't think of why you would want to do this with bullet behavior when platform is easily good enough and glitch free). If you want to change the player into a bullet later then disable / enable the behaviors at the appropriate time so that they don't conflict.