Moorsbus 2017 route and timetable info is now online with the 2017 season starting on May 1st (May Day). http://www.moorsbus.org/2017-timetablesfares.html
Arriva North East will operate services M1, M2, M3 and M4 on Sundays and bank holidays this year (M2 and M3 will be Darlington operated and presumably Redcar depot will do the M1 and M4).
Additionally on Sundays and bank holidays, Reliance Motor Services will operate the M5 between Easingwold, Stokesley and Helmsley (and I think a few M4 runs between Helmsley and Sutton Bank Visitors Centre) whilst Stephensons of Easingwold will operate the M6 between Malton, Pickering and Danby plus the M7 between Pickering and Low Dalby.
On Saturdays and Mondays Stephensons of Easingwold will also operate services M8 York - Malton, M6 Malton - Pickering and M3 Pickering - Danby.
Arriva North East: Upcoming Service Changes