Anytime in law where you talk about "intent," you either have to come up with a few objective standards that stand in for intent since we can't actually read minds or travel through time (and then, often, a judge can decide as a matter of law whether "intent" was met), or you have to ask what the "reasonable person" in the same situation as the person in question would have intended, or something along those lines (and then it becomes a question of "fact" and you ask a jury to figure it out) -- or is it what a reasonable observer would think the actor intended, upon observing the actions?
So anyway, the question really isn't what OP intended, but what intent his actions manifest.
I still say that leaving a bike somewhere a month doesn't manifest an intent to abandon, since I sometimes go a month without riding a bike. But the situation is different if it wasn't locked up, or was in someone's backyard, etc, which later comments make me think is the case. I need pictures.
And whether or not you'd be justified in taking a bike back, don't you wonder if maybe the people who found the bike might have needed it more, economically? That's a different question.
I am reminded of the Simpsons "Bobo" episode.
