Anyone who survives long enough with this weapon to reach a settlement would be best trading in for a real weapon, such as any of the others in the weapons category (see category below).
Training with the BasicsEdit
The BB Gun should never be considered a stand alone weapon. It is in no way a gun meant to be used in combat. In fact, the only serious use of the BB Gun would be for training, trading, or using the base parts for some means of construction.
The problem is, the BB Gun was never meant to be fatal. In the Pre-War days of the past, children would use this to shoot at one another (much to the horror of their mothers, who realized that such antics are dangerous despite the weakness of this weapon), and obviously they weren't trying to kill each other, they were merely attempting to hit the opposing team member and thus win the game. Some sources claim that this was a form of early combat training, but do not be fooled by these pseudo-intellectuals. The BB Gun was nothing more than a toy, and thus should be considered on this.
However, due to its rarity, the BB Gun can be a good collector's item and thus a good item to use during trade. There are reports of some giving these guns to their children, and training them with this, as well as using a BB Gun to train early guards or soldiers before combat as not to give them live ammunition.
But as was said, one can get a good price for this rare find, a good exercise, or a good means of repairing a lamp or gun or pipes, whatever can find use for the contraption. Just please, please, don't try to kill anyone or anything with it. You will surely fail.