I'm not sure there are many 'bus' services long enough for this to happen now, but would have thought it's not uncommon with coach services to avoid overnight stays being needed.
Although Reading Buses' 701 / 702 (Reading - Legoland - Slough - London) used to (may still have) some duties done by Slough based Thames Valley drivers and Slough based buses, but they all seemed to take meal reliefs at Slough, so some change-overs would involve a Slough driver handing over to a Reading driver or vice versa. I'm not sure if any buses changed ends from one day to another for maintenance purposes, but buses (until recently) only started from Reading early mornings and got back late evenings, so there must have been some Reading drivers needing to travel from / to Reading without a bus - not sure if this involved a staff car or travel by train.
Historically, there used to be some quite long distance services operated jointly between Southdown and Maidstone + District, as well as the 'Heathfield Pool' services, route 122 was Gravesend - Tunbridge Wells - Brighton. I understand that buses worked through, but crews / drivers didn't do the full journey, with changing over at Tunbridge Wells, so part of a M+D crew's duty could involve a Southdown bus and vice versa.