Carrying the firearm isn't as hard as lugging around the ammo. If you are willing to pay range prices I guess you are OK with just the shooter. Bar bag would do fine. For a longarm you can look into the molded cases used on ATVs, or a less prominent solution could be one of those tubular cases graphic designers, architects and artists carry their stuff in so you don't scare any liberals or present yourself as an opportunity to any thugs. My favorite method though is a guitar case. Or for when I'm shooting the clays a Bass guitar case for the much longer shotgun. I'm too lazy to break it down all the time.

Again though the biggest trouble is the ammo, but if you shoot .22 you needn't worry at all.

while I wouldn't want to open carry on a bike (easy target for a hit and run) I had noticeably less problems the few times I had to bring a crow bar to work and had it lashed on the rear rack.