There are a few examples of this
1990s Lothian used to run a 68 from Portobello to Mayfield in Midlothian that didn't seem to serve any purpose (I think about three journeys a day, early morning to Mayfield, returns from Mayfield in the early evening)... but the timings matched up with the express service from Mayfield into Edinburgh and back again later in the day - current Lothian are quite good at contra-peak services, but the nature of Edinburgh (where the city centre is so expensive that lots of offices etc are on the fringe of the city) suits those kind of routes
Here in Sheffield the southern end of the 20 is a bit of a "two side of a triangle" service (looping back from Graves Park to serve the Gleadless Valley (finishing at a classic post-war housing scheme turning circle with pub/ Chemist/ "convenience" shop - the Gleadless Valley is so untouched by the twenty first century that it's the filming location for some of Channel 4's "This Is England" programmes, set in the 1980s) - but the early morning journeys run from Olive Grove depot out of town up the Gleadless Valley rather than not in service. It's a different thing in the evening, partly because there are more buses on the road generally, partly also because it'd be more confusing to have Olive Grove as a terminus?
Stocksbridge features on railway threads from time to time - the town is about ten miles outside Sheffield - in the South Yorkshire Transport days the early/late Stocksbridge services started/finished at Catch Bar Lane, by the Sheffield Wednesday ground, because the service was operated from Herries depot. The move to one big depot in Sheffield (Olive Grove) meant services running all the way to/from the city centre.
Stagecoach took the services over from First around ten years ago - the service operated from their Ecclesfield depot, which is about as close to Stocksbridge as it is to central Sheffield (given the speed of the Stocksbridge by-pass, it's probably closer). They ditched the early/late journeys. That means we have the situation where First have the tender for early/late/Sunday services. There are three trips in the morning that arrive at the Stocksbridge terminus at 05:48, 06:48 and 07:48 (the first Stagecoach service arrives at the terminus at 08:08). But the tender only requires First to run journeys from Stocksbridge back to Sheffield at 05:50 and 06:50. There are Stagecoach services starting at Stocksbridge at 06:06 and 07:02 (before the 08:10, formed by the 08:08 arrival).
So First are paid by the PTE to run the service arriving into Stocksbridge at 07:48 which runs empty back down the Don Valley into Sheffield just ahead of the commercially operated 08:10. Looking at Bustimes today, the vehicle then formed the 08:30 service from Sheffield Interchange out to Tinsley (
https://bustimes.org/vehicles/246676?date=2022-02-18#journeys/221730774 << link shows the X74 from Sheffield to Tinsley)
It makes sense to someone but we have a situation where Stagecoach only register the journeys that they can operate at a profit, but the PTE want a proper service in both directions, so First run a tendered service up the valley to get in at 07:48 but then it has to run empty back into Sheffield at rush hour because Stagecoach are running their commercial service down the valley at that time (i.e. Stagecoach run empty to Stocksbridge to then run commercially into Sheffield, so taxpayers fund First running a service to Stocksbridge which then runs empty back down the hill)... it's maybe only a minor thing but it feels a wasteful example of our fragmented bus industry, where each party is doing what's best for them (I'm not saying that Stagecoach should run early morning contra-peak services at their own cost, I'm not blaming First for taking the subsidy, I'm not blaming the PTE for wanting to try to give Stocksbridge a proper service in both directions, but the combination of everyone acting in their own interests means we essentially have one operator running empty in one direction because the other operator is running empty in the other direction, and First are running an empty double decker into central Sheffield for half past eight in the morning when passengers struggle for seats in the morning rush hour on other services)
The Tinsley service I mentioned above (which the First double decker runs onto) is another contra-peak service - First closing the Midland Road depot in Rotherham has forced/encouraged them to be creative with the amount of dead mileage that comes with operating all Rotherham services from depots in Sheffield/ Doncaster. So the X74 is a contra-peak service from Sheffield city centre to the Parkway Industrial Estate and then the Advanced Manufacturing Park etc at Tinsley -
https://bustimes.org/services/x74-sheffield-rotherham - rather than running everything empty from Sheffield to Rotherham you can be creative with the diagrams - even if it only picks up a handful of passengers it may be cost effective
Does Bristol still have the 53 (?) for placing journeys between the depot at Temple Meads?