Check this out:
Notice how the ball squishes, and stretches? You want to do that with your sprite's animation.
Set the sprites position with a sine behavior, and use the ABS() so you get an absolute value... this will make it bounce rather than bob up and down.
You can do the above with a lerp too but i am not in the lerp kind of mood right now. Ashleys Sine behavior is much easier to use.
Now you just have to add a little to the sprites +X or -X for the actual movement.
Press rightArrow ----> set Sprite.Position: sprite.x+1
Press LeftArrow ----> set Sprite.Position: sprite.x-1
Tweak the 1 for the speed, the 1 means 1 pixel per frame.
You can post a picture of the event sheet?