The 2011 version of 'South Riding' stars Anna Maxwell Martin and features two buses carrying the fleetname 'York and Eastern', but neither is native to Yorkshire, and both are slightly too new for the 1934 setting.
Episode 1:
Seen from behind and inside as Anna Maxwell Martin rides it is North Western Road Car 452 (AJA152), a 1939 Bristol K5G with Willowbrook body.
Episode 3:
Another North Western bus seen from behind and inside is 372 (AJA132), a 1938 Bristol L5G with Burlingham body: