How do I pay off my bounty when the only options are to fight back or be arrested?
Are you sure this isn't part of a quest?
This happens in a Markath quest, where going to jail starts the next stage of the quest. Details are in the spoiler below.
This quest
You can't. If those are you only options, then your crime was so severe that a mere bounty won't satisfy the law-keepers. Your options are to go to jail (where your bounty will be wiped clean) or die.
Afterthought: Third Option: KILL! THEM! ALL!
If you have this then your bounty exceeds your current gold.
Travel around, you will eventually meet a bounty hunter who will offer you to pay your bounty + 10% finder's fee, then your bounty will be cleared.
You can try console commands to 'force' paying your bounty.
Make a save game first, and then in the game, open up the console by pressing ~, then click on one of the arresting/assaulting guard(s). The guard's RefID (a bunch of numbers) should show up in the screen. After that, type in paycrimegold in the console. That should put you just outside the nearest jail of the hold you're in, with no more bounty on you while still keeping your stolen items.
More info on the paycrimegold console command at the UESP wiki's "Console" article.
paycrimegold - Pay the bounty for the faction targeted NPC belongs to (the bounty gold will be removed from your inventory). The first 0-1 choice refers to being sent to jail: entering 1 will let you be teleported to the respective faction's jail, entering 0 won't. The second 0-1 choice refers to keeping your stolen items: entering 0 means you do not lose your stolen items, entering 1 means you do. If you don't add any choice you will be sent to jail without losing your stolen items. The faction ID is needed if you can't target an NPC. May also help in case guards attack you on sight.
Note that if you don't have enough gold, you can also use the console to add gold to your character. The console command to do that is player.additem f x where x is the amound of gold you would like to add.