Inside 10 yards, you can hit rabbits with shot loads out of your rifle. After that its a wish and a hope, as the rifling spirals the shot load. Any smoothbore barrel can be used to shoot shot loads.
I don't know what you are talking about by using the letters, " bb ". Are you actually asking about shooting lead BB shot in a smoothbore? Why would you want to use such large shot in any gun for hunting rabbits? Normally, #6 or even #7 1/2 shot is all you need to kill rabbits out to 30 yards and beyond, even with a cylinder bore shotgun shooting Black powder.
If you can't get within 30 yards of a rabbit, don't take the shot! Since I showed my ex-wife how to walk up to within 6 feet of a wild rabbit, I find it difficult to believe anyone can't work within 30 yards of a rabbit.