There IS a wayIt is possible to see your current bounties in skyrim...It works both on consoles and PC versions, you just must go Go to your quest, general stats, system screen...There on:
Quest Menu > General Stats > System Screen
General stats you can find, under crime if u go bit down and, you can see your current bounties. If there are no cities shown up, it means uyou have no bounty. It's that simple. :)