Aragorn the Ranger

[Nazgûl-king]

I always thought Aragorn had a bow and was a pretty good archer, of course I saw the movies first so that might have influenced that but… anyway a bow would have been usful for hunting.

[Legate of Amon Lanc]

I'd say it this way: What we know for sure is that Aragorn did not have the bow after he left Rivendell. Whether he had it when he met the Hobbits can be a matter of speculation, based on the arguments mentioned above. The main of the "pros" would be that he speaks about hunting, main of the "cons" is that we are never told he had a bow and when the hobbits meet him at the Prancing Pony, and he is with them in their room, he definitely has only a sword (and even broken). Now where would he put the bow meanwhile? Definitely he would not leave it in the common room. Unless he had another room rented, or some secret stash where he kept his bow, I would conclude that he didn't have any.

Concerning the period after Rivendell, this makes it pretty clear:

Originally Posted by The Ring Goes South

The Company took little gear of war, for their hope was in secrecy not in battle. Aragorn had Andúril but no other weapon.

[Gwathagor]

Aragorn might have had a bow with him prior to the Ring Goes South, before the Nine Walkers leave Rivendell. Thereafter, it would have been an unnecessary encumbrance. Bow-hunting would have taken time which the Company did not have.

Regardless, I am inclined to think that Aragorn could have gotten along just fine without a bow. Foraging, and perhaps laying the occasional trap, would have been more practical for a wandering Ranger who was constantly on the move. Also, it is part of his nature as a heroic character to carry and wield no other weapon but his ancestral blade.

However, I think Gandalf does describe Aragorn as not only a great traveler, but a great hunter as well. This could mean either that he was good at killing wild animals, or that he was simply good at tracking. The latter makes sense, as Gandalf relies heavily on Aragorn in the tracking and eventual capture of Gollum. I'm sure that Aragorn would have been a good wild-animal-killler in any case, but if Gandalf was choosing to specifically describe him as such, then Aragorn almost certainly carried a bow.

[Legate of Amon Lanc]

My conclusion is that Aragorn usually carried and used a bow. However, with the Fellowship he did not bear it, and in my personal opinion (as explained above) before in Bree, for reasons unknown, he also did not have it with him.