For the longest time I have had a bounty of some 40g on me, and assassins have been out to get me (they always have a hit contract signed by Astrid). The only thing that I can think of was stealing a bandit's horse. It was my first visit to Whiterun, and on the west side of the promontory on which it lies is a hollow with a camp of bandits. They have a wagon and a horse. I cleared the place out, mounted up and rode to the gates of Whiterun. I may have been on a bounty quest for the Jarl. I have since learned that stolen horses report to any and all guards! Still, the horse ran back, so it was no permanent loss. Besides, it was a
bandit's horse!
Last night I was SE of Riften and, having come under attack multiple times by creatures of the night, was jumpy and overly cautious. So when I saw a figure standing in some ruins, I shot him. Turned out to be a hunter, and a 1000g bounty was on my head, that is until I shot his dog, then it was removed. But it still shows in my General Stats. I wish there was a way to show exactly what the current bounty is and why.
BTW, I've done both of the quests you've mentioned without any bounty being placed on me.