What size prey are you feeding her and how often?
Why on Earth on your handling her so much? She does sound thin and needs to be eating and resting not spending energy being handled.
A young BP should be handled for 5 minutes at a time or so, every few days, if healthy. They stress easy and again, are often pet rocks when not being handled, so they do not spend a lot energy normally.
I recommend basically leaving her alone and getting some weight on her and then worry about handling.
On the live vs. F/T issue, you might be able to switch her at a later date, but right now you need her eating, so give her what she will eat.
EDIT: I realize this may sound a little harsh, but we are here to help. There can be little margin of error with young snakes and we want your BP to thrive.
Feel free to ask for clarification on anything.