I believe in London, operators tender for individual routes. It’s normally a five year contract. The fares are set by TFL, not sure about the timetables.
I know that when I worked for Stagecoach in London, when they won one of their new routes, they actually added another bus to the frequency.
I guess an operating company can keep a route or win one by default, if no one else bids for it.
The TFL model is unique to London though.
Yes, broadly speaking, each TFL route is a separate contract (there are a few that are bundled together, and most night routes are attached to a day route, although operators are usually asked for a price for doing the day route on its own - even on a '24 hour route', the night bit is a separate entity contractually) - although operators may offer joint bids, where they can do route A for X price, route B for Y price, or do routes A and B for a combined price of Z (which offers a discount.)
Yes, fares and ticketing is entirely TFL's responsibility, ticket equipment (and some of the other tech) is owned and supplied by TFL. When cash was taken on bus, the revenue went back to TFL (as in operator would invoice TFL for contract price minus revenue each month - don't think they physically had to send cash to TFL!)
Timetables are not exactly set by TFL.
TFL detail the route, and issue a specification along the lines of 'on Sundays, first bus from A to B should be no later than 0600, last bus should be no earlier than 0015, frequency of departures should be no less than every 30 minutes between 0600 and 0900 and after 1800, and no less than every 20 minutes between 0900 and 1800' (obviously this is a very simple one - it can get more complicated on weekdays with some routes having higher frequency in one direction, and most routes have 'pinch points' e.g. departures from A towards B every 10 minutes, but buses must be every 10 minutes at X in the middle of the route (while running time is increasing as the peak hour builds up.)
It sometimes saves a few hours of bus and driver time to run the first bus a bit earlier than specification or last bus a bit later, e.g. if specification would mean buses leaving each end at 00 and 30, but running time is 32 minutes each way - you could do that with 4 buses and 28 minutes stand time at each end, but it's more efficient to start a bit earlier from one end and do it with 3 buses.
The operator is expected to work out running times based on data / observations of existing journeys, what margins and recovery time they think are right to meet the performance standards, and balance the expected bonuses for exceeding targets against the possible resource costs of doing it.
This can sometimes mean adding a bus compared to current - although TFL may question it if an operator puts in a timetable / vehicle requirement that they think is unrealistically tight, or uses far too many buses.
Contracts are usually for 5 years with an extension of another 2 years being offered subject to meeting certain targets.
Yes, I think it's possible for routes only to get one bid (in London and elsewhere) although there's few parts of London where there's a true monopoly, and many operators will bid for routes a bit outside their normal patch just in case. I'm not sure what TFL would do if they only got one bid for a route and the operator was clearly taking the proverbial. Or for that matter if a route got no bids at all - I presume they can make emergency short term arrangements, and try again with the tender, although I'm not aware of this happening.
Depending on what inflation clauses are in the contract, operators are taking a risk that costs will increase beyond what the contract allows, and of course a risk they have been over-optimistic in their sums. There have been one or two London contracts over the years where operators have not been able to get enough drivers on the rates they have tendered on. I think TFL would be within their rights to ask questions before awarding a contract if one operator's bid was very significantly lower than others (through optimism or dubious maths.)
