The question fairly often crops up on here about travel from York to Thirsk [for All Creatures Great and Small] and (less often) Helmsley.
The answer is to use Reliance Buses.
As of yesterday Reliance has ceased operating all their Stage Carriage Public bus routes- they have all been taken over by Transdev York (trading as York and District)- routes and vehicles.
For the the being routes and timetables remain unchanged but that may change in the future as operations are centralised in York rather than the old Reliance Garage at Easingwold.
And of course you need to know which company livery to look for, and where to find timetables.
One side effect is that the services are now within the Transdev ticketing scheme, including day and longer period tickets. So Transdev system wide day and weekly tickets now cover from Preston and Manchester to Scarborough and also up to Thirsk and Helmsley.