(13 Mar 2015, 10:30 pm)Jimmi wrote Probably.

If you could get a train from Newcastle Central Station to Darlington Rail Station to get there for the time the bus leaves Darlington Tubwell Row at 0945.

Some train times doing a quick Traveline search on Sunday May 17th as an example with the times leaving Newcastle:
0755 East Coast (Virgin) - Arrives at Darlington for 0826.
0800 First TransPennine Express - Arrives at Darlington for 0830.
0855 East Coast (Virgin) - Arrives at Darlington for 0926.

Darlington Train Station is roughly 5-10 minutes walk to Tubwell Row although the timetable says the bus stops also outside the train station on Victoria Road at 0947.

Dalesbus timetables can be viewed here.
http://www.dalesbus.org/