smackababy
Lifer
In reality though, you would still need a supply of quality bolts. He has sent hundreds of bolts down range at zombies and not been able to pick them back up. That means picking through homes for bolts... which probably is not very productive. So you would have sporting good stores which may or may not have decent supply of bolts versus standard bows and arrows.
You could make your own, and at least you'd be able to find the supplies for points and such more readily than bolts.
*But this is T.V. I think they've shown plenty of time him recovering his bolts so at least they sort of address part of the problem.
In the show's universe, zombie heads are soft enough a person can smash it with pretty much anything. So, a bolt isn't likely to break upon hitting a zombie and he does recover them a lot.
I agree, it isn't the best choice, but it isn't a horrible one. You can remain quiet and kill things at a distance. Making bolts isn't something entirely out of the realm of possibility and it is easier to have ready to fire than a bow.
A good compound bow is likely your best bet, if you are proficient with it. You can make arrows in your spare time, at least ones viable for shorter range shots, and you can hunt at range. Few things are going to beat a good AR-15, but bullets will only become increasingly hard to find as every day passes.