Retired insurance agent here - not from Florida. But generally, If YOU crash your bike and submit a claim to YOUR insurance company, and you and they agree that the repairs would cost more than the Blue Book value, then your insurance company pays you the Blue Book value and they take the bike to be sold as salvage.
But that's not what's happening here. You're not dealing with your insurance company, your dealing with hers. So in this case, it's a matter of how good you are at negotiating. If I was the claim adjuster for the woman's insurance company, I'd be happy to pay you the Blue Book to close out the claim and let you KEEP THE BIKE if the repairs are gonna be close to or over Blue Book If you can get them to agree to that, you can use the money to buy used parts on eBay or wherever, install those parts at a labor cost of zero dollars, and end up with a bike that still has a clear title not a salvage title. And probably leftover money in your pocket.
Your first step is to get the bike into a BMW dealer for a damage appraisal. That will cost you a few bucks but without it you have no way to argue your case. The appraisal done by HER insurance company is useless to you.
Of course, if you don't want to fuss with it, that's your privilege. I just wanted to point out that the other company can't "force" you to give up the bike and title as salvage. It's a negotiation.
Also, if they try to tell you some bullshot about "no fault" they are trying to bamboozle you. No-fault in Florida only involves injuries, not damage to vehicles.