Not sure of the mechanics for bounties.

Example: I'm in Markarth. I break into the stables for a quest. At the foot of the stairs is a dog. The time is about 3:45am. Everyone is asleep except the dog.

I break into the stables hidden, so no issue there.
Nobody in the house awake, no issue there.
I have to shoot the dog to keep it from alerting anyone. I see a 5g bounty applied. OK, no problem so far I guess.
While hidden, stealthed, a guard pops through the door behind me and arrests me.

So. I don't understand how the bounty is applied if I am not caught by anyone awake.
Not sure how the guard came looking for me either.

Any input on this?

To add to this: I sneak in and don't kill the dog. Yet the dog "spots me" and I get 5g and arrested.

harry potter and his invisible cloak

i also have an issue when i snipe someone while im sneaking high up in the mountains and it says im hidden but whenever i kill them it gives me a bounty although noone was anywhere near me

Never had this problem. Your main problem may be people finding the body and then reporting you, or you don't instantly kill them and so they call out for help when hit.

Well, the dog was one-shot so that shouldn't have been it. Not sure what's causing the issue.

Workaround was to wait until daylight and pickpocket the key off the stable guy.

Then wait for a quick hidden opportunity between the stable owner, the stable worker and the dog to pop inside the stables. Once in it was easy to get.