I was looking at this thread about such a journey- https://community.ricksteves.com/travel-forum/england/travel-from-manchester-airport-to-sedbergh
Although I know the OP has now travelled it is important for the record to correct that thread as the bus information is (and was then wrong) due to just googling an answer- that happens frequently on this forum, sadly.
Woofs Buses have not run for many years now, and were not running two years ago. Unfortunately the website is still up.
On a Monday to Friday you travel to Oxenholme and then travel on the Stagecoach 563 bus (bound for Penrith)- that is a very new route.
But still running, as they were 2 years ago, are the Western Dales services S5 on a Friday (to Kirkby Stephen, and from Kendal, not Oxenholme) and the S1 on a Wednesday and a Saturday- some S1 journeys extend beyond Sedbergh to Dent and Dent Railway Station.
The Western Dales services were a part replacement for the withdrawn Woofs route.