Did Bear Bryant ever beat the University of Alabama as a coach for another school?

No. Prior to taking over at the University of Alabama, Bear Bryant was the head coach of the University of Maryland (1945), University of Kentucky (1946-1953), and Texas A&M (1954-1957). Bryant coached teams against Alabama twice, both as head coach of Kentucky. On October 19, 1946 Kentucky lost 21-7 and on November 1, 1947 Kentucky lost 13-0.