I know of at least one local authority who are agreeing an amount with the bus companies at the start of each financial year to cover predicted amounts to aid their budgeting for the year.
Eg council offer operator £3m to cover all concessions for the whole financial year. The amount is based on typical average usage of the pass in previous years.
I've been following this thread with interest, as I was involved (at bus company level) with concessionary fares reimbursement (on and off) from 1986 to 2020 . . . so I know a bit about it!!
Back in 1986, a "generation factor" was set, pretty much countrywide. This said that 70% of the single fare would be paid as reimbursement for each pass journey; the discrepancy was to allow for pass holders making extra trips because they only paid half-fare. It was impossible to quantify this, even with early electronic ticket machines passenger data, but it was felt to be reasonable.
Fast forward to 2008, and Gordon Brown's efforts to secure the "wrinkly" vote with free travel for the over-60s . . . initially this was to be funded by the Treasury, but rather quickly it was found to be far too expensive. The qualifying age was to be raised towards 66, and the monies available were reduced. Such monies that were paid over were not "ring-fenced", so some Local Transport Authorities would use the cash for other reasons. The 70% generation factor was retained, as there was still no way of quantifying it!!
The DfT made available a "Revenue Apportionment Tool", for LTAs to use . . . some did, some didn't. It was horrendously complex, and soon only consultants could understand it!! The LTA that I was concerned with took a different route (pun not intended) . . . a sum of money was agreed between LTA and operators, and this was apportioned route by route based on the average single fare for that route.
So . . . if a route had an average adult single fare of (say) £1.20, then around 60p would be paid; if the average single fare was £2.00, then around 100p would be paid. The number of season-type passes was also taken into account (ISTR that weeklies were assumed at 9 trips/week; monthlies at around 35 trips/month), so the "average fare" was pretty much understood. Note that the 70% generation factor was now around 50% . . . quite simply, this was all the LTA could afford (remember that the Treasury had slashed the relevant funding).
Every year, negotiations would take place . . . the LTA would say "we can't afford any more", the operators would respond with "we'll start cutting routes then", and a figure would be agreed that (sort of) satisfied each side.
The beauty of this is that bus operators can be pretty sure of the reimbursement, so budgeting is more accurate. With the RAT, a quiet month for passengers would mean lower reimbursement.
Quite how the £2 fare has affected matters, I'm not sure . . . during Covid, ENCTS reimbursement was paid at the previous rate, but I expect that's finished now.
Happy to answer any specific questions, if I can . . .
Just to add to my earlier comments . . . as far as cross-boundary routes are concerned, the authority in which the journey starts pays the piper!! So a journey from Watford to Luton will see Herts CC pay for the usage; a journey from Luton to Watford will see Central Beds pay. The operator would need to keep fairly accurate records of which pass boards in which County, but current ETM software can deal easily with the reports required. Thus applies for local journeys within Herts CC with a Central Beds pass . . . the hours of acceptance may be different, but the payment principle is the same.
I don't know how cross-border journeys England <> Scotland or Wales are accounted for . . . theoretically in the same way, although England passes would NOT be valid for local journeys in Scotland . . .does anyone know for sure??
As far as gross-cost or net-cost contracts are dealt with, I'm not sure now . . . it always was the case with gross-cost contracts, the operator was paid an agreed pence per mile, and ENCTS reimbursement went from LTA direct to LTA. With net-cost contracts, as the operator retained the revenue, they would need to receive the ENCTS monies, so would treat the route as "commercial" in that respect. There aren't many net-cost contracts now . . . the risk for the operator is too great.
And don't forget Bus Service Operators Grant . . . a route run commercially will receive this from DfT; a contracted route will have this paid directly from DfT to LTA. it's all income!!