Bbl is the standard abreviation for the word barrel. But not generally in the context of gun barrels, rather in containers that hold liquid. Oil’s $103/bbl, etc. I’ve seen gun barrels referred casually at bbl ever since I was a little kid. It’s pretty standard practice, actually.
I think that chad is correct about bbl being a standard abreviation for barrel. I have always seen it printed as bbl on firearm boxes, and manufacturer’s descriptions of their firearms. It certainly fits better on the boxes.
I now this is old but here is a little tid bit. Bbls is a brewing unit of measure. The British came up with it. I think it stands for British barrel unit. It is equal to 31 gallons. Ever wondered why kegs were 15.5 gallons 🙄 . Its because they are half a barrel. So next time your in your favorite brewery ask the Brewer how many bbls the kettle is. If he is worth his salt he will know. Oh this is the only industry that uses this measure. FYI a hogs head is a 27gal bbls. For those who were curious.