Up until a few years ago, Bama and Tennessee were on top of the NCAA in bowl appearences and bowl wins.
But as of now, UT trails BAMA in bowl appearences and trails Bama and USC in Bowl wins.
As far as consecutive bowl appearences, I think FSU currently has more than UT. ANd I think there is one more school in there. I think Ohio St. But Im not sure.
Sorry I couldnt be of more help.