This discussion popped to me when I realized my current char has a lifetime bounty of 2348....
So, what is your highest?
Where is that stat? Are you just looking in General Stats -> Crime ?
I have about 36,000 on one of my characters
4248, I think. But I cleared it by killing everyone in the room. Not an easy task, I can tell you that. Had to drop them all before they could so much as utter the word "guards".
24180 :P