Is there a doyen or some way to get rid of bounty in shivering isles whit out paying the guards?

Or a mod.

could always cheat if you want it to be done quickly

player.payfine

I was thinking a cheaper way to do it.

ok, player.payfine removes your bounty, it doesnt not take your money to accommodate the amount of your bounty, it will reset it to 0, you wont loose money, but theres a possibility of loosing stolen items if you do it this way