Hi LAF - You sound like a very mature 22 year old. This is good, but its also your problem.
Your lady was with her ex for 4 years, meaning she was 18 years old when they got together. I assume she is not that experienced with other guys. She may want to play the field soon. She will also be licking her emotional wounds for a while and you run the risk of being her 'shining knight'--not a good thing to be if you want a longterm future with this gal. There is a sticky about this on the main forum page. Suggest you read it and post your thoughts.
Now, if you were 42 (not 22), my advice would be to take her on a quiet date and tell her, clearly, how you love and admire her and want a longterm relationship with her. I wouldn't even worry about the FWB thing, its just a label after all. You know someone loves you by their actions, not their words. That's how I can tell just from your posts you are in love with her. Most guys would be thrilled for the sex, but for you that's not enough you want her heart so, yea, you love her.
Here's where you are hooped tho, if you carry on this way:
She is still toying with getting back with her ex. She hasn't made a decision to move on. This is bad news for you.
There are only 2 ways I can see to proceed, and like WU said, you won't like either:
1. Break off FWB with her. Don't be an ass. As her friend, tell her the truth: you are falling for her and you think she is still hung up on her ex. Say you want her for yourself but have to protect your own heart until she is ready for you (by this I mean the 'you' that is a couple).
2. Continue FWB, but realize you are going to lose her, longterm. Right now you are a rebound, and (read the Shining Knight sticky), these *never* last. No exceptions, bucko.
Hope this helps.
Second thoughts can generally be amended with judicious action; injudicious actions can seldom be recovered with second thoughts.
--Cyteen by C.J.Cherryh