JOhnboy,
I have been mulling that one myself. I am thinking about something more on the side mount idea. I have a scabbard from the ATV that I was going to use. I often ride over to a friend's to shoot and had rather ride the bike.
As a side note. when I was with him we went to a gun shop and I bought a .22, semi-auto. It was a cheapy (but my son loves it) but it looks like a M-16; all black, carry handle, pistol grip, box type mag, etc. Anyway, how to get it home, since I am on the bike. I used the strap on the rifle to put it on my back and off I go. Made it home with no incidents.
But would not want to do that every time.