Would it be plausible to level up to 55 on random BG's?
However I was under the impression it wasn't a speedy option. Did the buff the XP gain or anything like that?
unless they were really sneaky about doing so, no. The have nerfed the EXP twice from what I've been told in BGs.
As for other option: you are very close to going to Outlands, so where to quest is more tied to what side you play on, but if you are 56 still I would suggest Bad Lands, because when you hit 58 you can use the Portal right there in the zone to move on.
Once through, quest for exp but queue for instances but not randoms. Only run the instance one/twice to do the quests for the area. Do this all the way to 85 (I've yet to take one of my characters past 85 yet, but I'd assume you need to quest more 85-90).