I use the following setup:
1. Bike Pro wheel chock with a strap that compresses the front tire to the chock. This by itself is virtually enough to keep the bike upright if you hold down the rear wheel.
2. 1 soft tie to each handlebars, lightly strapped down to anchors in front of the bike. No need to make these tight at all, since the bike is being held upright by the chock/front tire strap. I put just enough tension on them so that they wiggle but wont wiggle enough to come unhooked.
3. 1 soft tie around each of the fork legs, just above the lower section (behind the protector). I cross the ties behind the fork and lightly anchor these as well to the front of the trailer...once again, leave some wiggle room...just enough to take all the slack out but they still flap around just a tad.
4. Bungee cord over the rear wheel to anchor points on each side of the tire to keep it from hoping.
Have transported the bike like this many, many miles with no issues.....will try to find pics if I still have them.