Are there any direct buses between Tiger Leaping Gorge and Shangri-La?

No need to go back to Lijiang. In Qiaotou Town (Huqiaoxia Town), you can take the passing bus from Lijiang to SL. Just wait at the local Long-distance Bus Station.

From Victoria Woodard's e-book "Over the Top: Cultural Treasures in Southwestern China (Adventure Travel Book 2): btw, I'm still reading Travel Book 1, and enjoying its generous amounts of information.: "The Frenchman carried Patrick's [partner of the author] pack to the other end of Qiaotou, because Patrick had broken his shoulder in a fall on the Tiger Leaping Gorge trail. WE WAITED A LONG TIME FOR A BUS TO ZHONGDIAN [Shangri-La]. Many minibuses offered to take us ... we refused because our guidebook said Shangri-la was Dequin, a different town about 9 hours northwest of Zhongdian on the road to Tibet. Although we would have loved to travel into Tibet, we needed to go north from Zhongdian, not northwest, in order to return to Chengdu and our teaching jobs."

By the way, a few pages later, Victoria Woodard and Patrick [Diehl] learn that Zhongdian IS Shangri-la! Zhongdian had renamed itself Shangri-la. Then there's a nice digression about where the name Shangri-La came from in the first place, including a pronunciation tip: Evidently "Shawn Gorill-LA" comes pretty close.