You could screw in a guide to hold the front wheel in but I have always just used a ratchet strap and tied the front wheel to the front of the trailer, works perfect if there is a little vertical support beam in the front of the trailer. Looks like yours has it.
Make sure to preload the forks as much as possible when you strap it down. As for the back end bouncing around just find two points to strap it down snug and it should be good. That way the bike will absorb a little of the bumps, might be easier on the bike.