Connect Tees Valley have uploaded the new timetables for the Darlington services, similar frequencies to the current offering from Dales & District although additional trips have been added on service 72, on weekday mornings there will be a 72 to Northallerton  departing from Darlington at 06:45 and an additional Monday - Saturday evening departure to Darlington departing from Northallerton at 18:10

29  https://connectteesvalley.com/data/timet...290419.pdf
34  https://connectteesvalley.com/data/timet...290419.pdf
72  https://connectteesvalley.com/data/timet...290419.pdf
610R  https://connectteesvalley.com/data/timet...290419.pdf

79 has a slightly revised timetable with a new trip departing from Richmond at 17:45, there's also a X79 to Richmond departing from Barnard Castle at 07:00 (how it takes just as long to get to Richmond as the 79 does even though it misses some of the villages out is beyond me) anyway, times can be found on BusTimes (will have to change the date to April 29th to see new 79 times): https://bustimes.org/operators/hodgsons