No expert on this at all, but I've done several thousand miles on a trailer and in a truck bed.
First thing, get a chock. They aren't expensive and are will worth having. The purpose of the chock is to lock the bike into an upright position. You can either bolt the chock down in your trailer or use a strap to keep it at the front of the trailer. A chock also works in the truck bed.
I use soft straps to attach the ratchet strap to the bike. I like to attach as close to the triple tree as possible. Sometimes I have to use the bars. If I do use the bars, attach as close to where they are supported as you can so you don't bend them. I attached the straps so they are pulling the bike down and forward. I like to compress the suspension about a third to half way. You hit some good bumps and the bike will compress itself and possible loosen or lose the straps. Be aware you can bend the bars, so if you use them, be careful.
I will also use the soft straps and tie down the rear on the frame or shock mount. These straps are just tight enough to keep the bike from going sideways if I hit a big bump. They aren't really holding the bike in.
I've used this method several times for thousands of miles without any issues to the trailer, straps, or bike.
Get a chock. Let it do most of the work, not the straps.