I don't know if BB willingly sacrificed the entire hospital. It's hard to say, really. He knew XOF would be after him, that much is certain, but did he know XOF would basically exterminate an entire hospital to get to him? Who knows.
As far as I can tell, the plan was to, once Venom woke up, have Ocelot meet them and get the hell out of there before XOF showed up. At some point after Venom awoke, XOF was tipped off (pretty much immediately) so they had to scrap that plan and BB had to get Venom out of the hospital himself. It seems to me like XOF getting to the hospital that soon and killing everyone was not at all according to plan. Although, again, it's hard to say.
Which brings me to a few questions:
- Who tipped off XOF that Venom has awoken?
- Who says "V has come to?" in the opening cutscene?
- Why did they kill everyone in the hospital?
- Why now? Why didn't XOF just kill them while BB and Venom were under?
As for #3, I think XOF got wind that BB was going to do his Face/Off thing, and probably decided to exterminate everyone "just to be sure" they got him. Quiet was sent to BB's known recovery room to take out the Boss himself. That still leaves the question of who was the snitch. It's also hell of convenient that XOF discovers BB's location almost immediately after he's woken up. Remember, Skull Face had probably been looking for 9 damn years.
tl;dr: I think BB and Venom were supposed to meet Ocelot and GTFO well before XOF discovered their location.