Aragorn the Ranger

[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.