I didn't really try doing this much before the patch came out, so it might have been like this before, but is there now a limit to how many bounties you can get from the innkeepers? I had re-rolled a character, and decided I wanted to try a merc for hire. After about two or three bounties each from the innkeepers in Whiterun and Riverwood, there seem to be no more available in those inns, despite waiting a few days before checking in. Falkreath has only given me one.

I seem to recall that before the patch there wasn't a limit, but like I said, I really didn't do much with them. Is there a limit per hold?

UESP says they can be repeated indefinitely.
So it might be a bug.
Have you tried talking to Jarls instead of inkeepers?

I'm thinking it is a glitch, like you said. I will try the Jarls, though.

I have not had an issue getting the Bounties. Did you get paid yet for the Bounty? That might stop getting a new one if you have not been paid for the last one.

Yeah, I turned it in. Still no new ones available, regardless of who I talk to.

I don't have any available in the Whiterun area, but I figured it was because I've basically killed everything. :shrug:

I have a feeling that the bounty that the innkeeper gives you, and the quest that the Jarl gives you, are the same. So if you get the one from the innkeeper, you won't get another one from the Jarl.

Not really. I discovered you only get 2 bounties from each inn and steward. After a long while, after the mobs respawn, you get the same bounties again. Unless we're talking Companion quests, seems they are really unlimited as they resort to "Give me something to do" and then some random mob spawns at a random location for you to kill.