That's what the storage charms are for.
Normally I'd agree, but it takes a handle item action for each retrieval due to the fact that it needs to be triggered. My guess is that most every DM in the world would wave that for pulling arrows but technically each time you want to retrieve an item you have to trigger the storage charm.
Not to mention that a Storage charm really isn't "bottomless" in any sense. There are two possible meanings you could take the descriptor of "bottomless" to mean: A container that can never be filled up, or a container that can never be emptied out. In the context of something like a "bottomless quiver", the intended meaning is generally the latter, but either way a Storage charm fails to measure up.
For the first meaning of "bottomless", the Storage charm fails because there is a fixed (and in fact fairly small) limit on how much it can hold. In fact, this limit makes the Storage charm a really poor way to model a bottomless quiver, because even a level 20 item with the Greater version of the charm can't even hold a full quiver's worth of loose arrows, as the charm is limited by item count. Storage charms are good for storing a smaller number of very large items, but not lots and lots of small things. At best you might consider a quiver or other container filled with arrows as only one item toward the storage limit, but that makes your Storage item a "quiver containing a dozen other quivers", which is quite a bit different from a "bottomless quiver".
And of course, the Storage charm obviously fails to meet the second meaning of "bottomless", because (as the name suggests) it only stores things put into it, rather than generating anything.
Even if you fudge the action requirements and
the item count limit (to count a given number of arrows as a single unit even without being in a container), a quiver with the Storage charm simply amounts to an unusually capacious quiver, far from bottomless. In fact, the only difference between it and just carrying a bunch of arrows normally is encumbrance.