I am not sure what safety concerns you have with a bike rack on the back bumper of the TT? That's where I have mine. If you tow with a pickup, the bed would be an option. The other option might be a bike rack mounted to the front bumper of your tow vehicle.
HA!....no dogs here, but the bike is a ton of fun. The platform is also good for carrying fire wood or my fire pit. I keep my generator strapped down all the time on it now. No more lifting it up and down out of the bunkhouse door.