I checked Traveline web site (which I've just done again now) and the only place it lists under the 555 timetable is Thirlmere, Kings Head. Theres no mention of a Thirlspot. The times you provided for your journey from Kendal bus station to Thirlspot, Kings Head are the same as those shown on Traveline web site for Thirlmere, Kings Head.
It seems one web site contradicts another with this. Google maps does not show Thirlspot but the Streetmap web site (which uses Ordnance Survey maps as is base) does. The Kings Head does appear to be near by but I can't find a bus stop serving it, which may suggest why Traveline doesn't show it either.
As dzug2 says, the online timetable for the 555 on Stagecoach's web site shows Thirlspot, Kings Head as a timing point. It also shows the service to run every 2 hours through out. My journey on from Thirlmere, Kings Head to Keswick, Bus Station used the times shown on Traveline. It shows the times for this Sunday (1st December) as every 2 hours between Lancaster and Kendal with an hourly service between Kendal and Keswick.
The only thing I can think of doing is for me to amend my journey to fit in with the times shown on the Stagecoach timetable. I'll hold off on resuming the game to allow other people to read this and say what they think.