droid, from one biker to another, Id say TDR air arms, I did just that, went to the gun shop, told them what I was after, and the guy, noticing I was clad in leather, recomended the .22 TDR, it splits into 3 pieces, stock, gun, silencer and all fits neatly in a oblong case that has rucksack style straps on it, very easy to transport, and connects together in seconds, you'll get a good 60 shots from it, before it needs filling up, so for shooting rabbits, no need to lug the bottle around on the bike, just top up before you leave home
as for permission, think outside of the box, dont just lo