The ONLY upgrade for BTTs that I am aware of is the complimentary 72/48 hour space available waitlist ones for MVPG/MVP. They can't be upgraded by miles, coupons, or even having a companion who is an MVP/MVPG buy an immediately upgradeable fare and then using the "hey, I can upgrade a companion" rule.
I ran into this making arrangements to take my daughter on a BTT to Cancun this summer. I was told the ONLY way BTTs (or companions of an MVP/MVPG flying on a BTT) get upgraded was through the 72/48 hour upgrade waitlist- so I stuck myself on the waitlist and am hoping two seats are available...