Are bounties infinite?
Solution 1:
Once you finish all the bounties in a single game, the only thing left to do really is Nephalem rifts. My wife spent the better part of last night doing all twenty-five bounties in one instance, and nothing new spawned.
However, if you just leave the game and start a new one, all the bounties will be refreshed, and you can continue doing bounties indefinitely that way.