It's been my experience (with Lydia only, I'm afraid) that followers using their default bow will shoot unlimited copies of the most powerful arrow in their inventory; give her a better bow, however, and she'll start using up her inventory's arrows. (To clarify: If you give her X arrows of any type (where X > 1), she will consume them until there is only 1 left, and then will continue to shoot that type of arrow without ever running out. Even if she has additional arrows of poorer quality, she will always use the best arrow available to her, and always in this fashion -- assuming she's using her default bow, of course!)
This is also backed up by forum posts such as this one (admittedly not entirely clear from this example, but was the best I could find).
Note that this doesn't just work for followers -- a great way to get as many arrows as you want is to reverse-pickpocket an arrow onto one of the game's practicing NPC archers, such as the soldiers in Solitude or the guys in the Thieves Guild: Put just one daedric arrow in their inventory, then go sit by the target and collect as many as you have the patience to wait for!
I've also seen Lydia shoot infinite iron arrows with a better bow, but in other situations I've seen her put the bow away because she ran out of arrows -- no idea what the difference is in this case.