It's funny, every time I participate in a SHTF scenario "what ifs" on the web I always recommend to buy a bow, lots of arrows, and practice until you'll are comfortable hitting a deer sized target at 75 yards (ish).
Then learn how to tune one and work on it.
Buy more arrows/broad heads.
My two oldest boys and I shoot at least once a week and both have taken a deer at 40+ yards, they're getting pretty good.
It's quiet (darn near silent) and 99% of the time I can just pick up my arrow and reshoot it at a later time.
However, I don't plan on going anywhere, so a BOB is a different story. A bow won't replace an AK for defensive purposes.
Another option is a good crossbow with scope/RD. Will put food on the campfire easier. Sling it on your back with 6 or 8 bolts.
I just like bows better. For feeding my family, not defending them...
The two loudest sounds known to man: a gun that goes bang when it is supposed to go click and a gun that goes click when it is supposed to go bang.