Shop around for a cheap set of gun holders, nothing fancy or expensive, they're handy to hold your weapon while stopped.
I used to ride with mine in them but stopped after seeing how much the gun/scope was bumped around when riding at any speed and/or hitting bumps. I never had a scope knocked off zero, but why take the chance. I now use the sling and either throw it across my back or lay it across my lap on short easy rides.
We used gun boots for a few years too but eventually stopped. One, they kept the gun dry during a ride in the rain which was nice. But once a gun gets wet while out hunting and you then put that wet gun into the boot for the ride home you'll have a wet gun every time you use the boot until it eventually dries out. Two, unless your barrel is really long and resting at the bottom, then all the weight of the rifle will be resting on the scope as you bounce over every bump.
