I used to transport my shotgun on a motorcycle. I would set the gun case crossways on the passenger seat & secure it with bungee cords. Certainly not the best set-up because the ends of the case are out in the wind, but it did work. If you have a Road Glide, you may be able to use something like the base plate that secures the top case on on the touring Harleys & mount the gun lengthwise where it would be more stable. John
I did it with a sport bike and a plastic case. With a break down gun secured in a good fitting case, Set the end of the case on the left passenger foot peg. Double bungie it to anything that does not move with the suspension. Where the case hits the grab rail bungie it there, threading through the handle to put more downward pressure on the foot peg. Bungie your shooting bag to the back seat. Looks a little silly but it works, and your body blocks the wind, everything stays narrower than you are. Make sure the stock and barrel are wrapped firmy in cloth to avaoid vibration scratching. The down side is that the case gets pretty beat up.
Used a Cabela's 36" soft takedown case plus some bungee cords and an SV650 last year to attend a local sporting clays shoot about 53 miles away (my truck was being borrowed and I figured, eh why not). Had a backpack on, plus another pack strapped to the pillion. Having it mounted that was was a bit uncomfortable (I had to arc my right leg a bit) but I made it without a hitch. After the shoot a buddy offered to bring it home for me; good thing too because it made lane sharing(splitting/filtering) down the 210 thru heavy traffic a lot easier ...
If I do it again, I'm thinking a Model 12 in one of those tennis racket looking backpack cases
I have carried a few different rifles and shotguns on my ultra classic and v-strom.On the H-D most of the time it is on the tour pack luggage rack or across back seat and tied down very well. On the v-strom across the back seat and on top the Al Jesse saddle bags,I have used the full length cheap-o wal-mart gun case the most it sticks out a little but not enough to bother anything.I have used an amera case but you have to pad with towels or it destroys your bike.A good bike ride to the club does help your shooting.ENJOY!!
Somehow I get this cartoonish picture in my mind of the gun crossways on the seat and the driver trying to ride through an opening not big enough.
I've ridden motorcycles pretty much my whole life of one kind or another. Unless you can get a gun scabbard(such as used on a horse) to mount to your bike, and be considered legal, it doesn't sound real safe.
back in the 80's I had a GoldWing, It had a luggage rack with a trunk on it. I kept my shooting bag in that, had hard cases on the rear and kept the shells in those down low. I laid my gun in a soft case across the top of the suitcase on the left side and then sat on the bike. I held the gun in with my left leg and it was nicely secure. The gun at the rear laid in behind the suitcase and wouldn't come out unless you crashed. It worked quite well but I only did this a few times during the summer.
As mentioned, Cabelas soft case which is too long anyway, and then put in a soft guitar case with backpack straps. Wear as backpack. Or strap to backseat somehow. Equal boxes of shells in each hard bag on sides.