Bows are made from renewable materials only (wood from trees, string from respawning spiders). Arrows however have a non-renewable material in the recipe (flint from gravel). You could take that into account when making your choice.
Arrows are renewable. You can get them from skeletons.
The problem isn't that bows aren't renewable, it's that there are a lot of enchants available for bows, and to get a really well enchanted bow can take some significant time and effort (not to mention, lots of XP). It's always a little frustrating when your OP bow (armor, tools, weapons) reaches its repair limit and you have to go through all that effort and XP to make a replacement. That's why Mending was such a nice addition (although admittedly, a pretty OP one).
Why they nerfed it with Infinity is a bit odd. If they really wanted to nerf Mending, they could have made it incompatible with Unbreaking [ducks].
I still think Infinity is the best choice (it's better to have arrows and not need them than the alternative). An Unbreaking III God-bow can be repaired several times before you reach the XP limit of the Anvil, and you can fire thousands of arrows before then.
I suppose the best way to know for sure would be to make one of each and see how often (if ever) you run out of arrows when starting with only 1 stack in your inventory with your Mending bow (since 1 or 64 takes the same amount of inventory slots).
I personally find that an irritating choice to have to make. I don't understand why Mojang thought this was a good idea? Fortunately I already have Infinity+Mending bows in my worlds, but if I ever lose them I'm gonna be pissed I can't make another.
I suppose I would have to go with Infinity over Mending. I'm a pretty crack shot with a bow, so I use mine a lot, and with Unbreaking III they last a good long while. I also like to use my bow off-hand while holding my sword so that I get the benefit of Looting III while using the bow (it's a great way to collect Ghast Tears and Blaze Rods).
As for the OP, I suppose if you have an AFK fish farm you'll catch enough enchanted bows to make another when your current one wears out, so I'd recommend Infinity. It's just nice to not have to worry about running out of ammo.