What do you call the interesting part of the line?
A lot of the tour groups just do Settle to Appleby, leaving the Eden Valley (north of Appleby) and Skipton to Settle out, although even Airedale from Leeds to Skipton is interesting.
But Settle to Appleby is only an hour, you also really should stop off at Ribblehead to see the very good Exhibition Centre there and hopefully the remains of the Shanty towns (and southbound a quick leap off at Garsdale to see Ruswarp the dog, an integral part of the history of the line).
Because of the tour groups packing the train out on certain morning and early afternoon departures at Settle, I would join at Skipton (25 minutes earlier) to beat them to it.
But effectively, if you are driving then you really have to double back. Skipton and Settle are both more or less straight on to the A65 for Kendal.
If you were only going one way to Appleby the sensible way to do it would be to look around Appleby (which the tour groups often miss, but quite an interesting town), then the service bus to Penrith.
While you certainly don't need a car in the Lake District in May, you can rent one from Enterprise at Penrith.
This is where having a car is a significant impediment.
In season (usually high summer) there is also an infrequent Tuesday only return steam special from York to Carlisle, and back- which was £98 return this year.