When confronted with a bounty, you have several options, which are detailed in the answer to this question.
In your particular case, you can't declare Thaneship. You've also indicated that you'd rather not lose skill progress.
In this case, you still have several options:
- If you've got cash on hand, you could just pay it off. The guards will leave you alone at this point. No harm, no foul.
- If you have some thief skills, you could get caught. If you sleep in the bed, you'll lose progress in some number of skills towards the next level, but if you break out then it's all good. This does clear your inventory, however, and you'll have to sneak to get your stuff back. Your "owned" items are returned, but if you want your "stolen" items back, you'll need to pick a pretty hard lock. In some cases, people have reported issues after having their inventory cleared. I'd suggest saving first.
- If you're "in" with the Thieves' Guild, you can bribe the guards, which is often cheaper than paying off a particularly high bounty. However, getting the bribe option requires that you've already completed some quests for the guild in that particular hold. Not something you could fix if you haven't done it already, but an option to consider for the future.
With regards to skill loss: you will not lose entire points, just progress towards your next point. So if your one-handed is at 50 and you're halfway to 51, you might lose that halfway to 51 progress, but you will not go from level 50 to level 49.
In my opinion, the far more irritating part is the glitches that sometimes occur when your inventory is dumped into the chest, and the potential difficulty of recovering any items marked as "stolen."