After several read-throughs of the book I am unsure how ammo supply is tracked. Are we supposed to check it every time we take an associated action? Or is it more like, say, Dungeon World where it’s abstracted and spending ammo is a consequence that can be laid down by the GM (or, I suppose, both)?
A bit of both. Ammo is abstract, each circle can mean anything from a single shot to a volley of fire running several seconds. We spend it for relevant actions when shooting, as a consequence (uh, your ammo gets wet, lose half of it), or more commonly, to make bombs. Yeah, players being players…
The skill description doesn’t require it, and as with everything FitD, follow the fiction. Then again, a single shoot roll may cover for several happenings, all with just the one ammo box you ticked at first. It’s a way for you to gauge the difficulty of an encounter. Planning and managing equipment is part of the challenge in BoB, so don’t shy away from it. In my games, players rarely run out of ammo, but I tend to use the same roll result for covering most of the combat, it’s just a matter of personal preference.