I think you ought to take a close look at the regulations regarding transport through states you are not licensed/permitted. I believe that it requires that the gun be locked in a case, unloaded, with ammunition in a separate location, away from the gun and case containing it. I'm not an attorney, nor have I played one on TV, but while locking it onto your bike with cable or trigger locks, etc, might be considered compliance with the spirit of the law, it may not comply with the letter of the law. I'd go for an enclosed, locked case. If it's enclosed and out of sight, a LEO or thief has no idea whether you have your lunch or a handgun in the case. Plus, keep in mind that a passer-by may go into hysterics at the very sight of the disassembled gun and report the presence of the gun to a LEO...after all, that nasty gun might assemble, load, then fire itself and injure an innocent child!!! (sarcasm intended). Why open yourself to that kind of aggravation.
I know every bike is different, but I have a nanovault with cable which attaches to the bike and the case fits into the saddlebag, out of sight. Only a couple inches of the cable is visible if you look closely. If I have to go into a building where illegal to carry, I can lock it up and know it's (fairly) secure, not subject to a quick grab. If going interstate, I have ammo and mags in another locked case in the other saddlebag. That works for me.