TL can be a slow journey. There is no direct bus from BB, and the TL busses are also the downtown disney busses (but there are 3 DD stops - Marketplace, Pleasure Island and Westside, and THEN you go to TL). Take any bus from BB to one of the closer resorts with only 1 bus stop (go Boardwalk or Swan/Dolphin), and then take a DD/TL bus. Your fastest bet would be a taxi, if you want to spend about $10 or $12
Whatever you do, do NOT change busses at Carribbean Beach. We made this mistake once trying to get to TL - you end up going to all 7 or 8 stops at CB - it will eat up a lot of time. For the same reason, I would also axe Coronado Springs, although it is not as bad.