Episode 1.21: Mirror Image
A young woman is waiting for a bus at a bus station near New York - when the bus arrives her doppelganger is already aboard:
Episode 2.28: Will The Real Martian Please Stand Up
A UFO is reported to have landed, and a busload of passengers shelters in a roadside diner. The bus is reportedly a Reo Comet:
Episode 3.36: Cavender is Coming
Made in 1962, starring a young Carol Burnett, this episode features Culver City (California) Municipal Bus Lines 4502, a GM New Look 4517. Incidentally this was the only Twilight Zone episode to feature a laughter track.
Burnett's guardian angel appears next to her on the bus - and briefly turns the bus into a carriage!
This understandably upsets the driver who announces his resignation from the bus line and dives out of the window.
Episode 5.2: Steel
Made in 1963, set in Kansas and starring Lee Marvin, this episode again features Culver City (California) Municipal Bus Lines 4502, a GM New Look 4517: