I covered a lot of this in post #8 (and apologies for repeating anyone else), but look at it this way:
Most flights serving Bournemouth are holiday charter flights, with a smattering of scheduled flights mainly operated by Ryanair. As such, these flights only run once or twice a week, and flight times vary by day. Naturally, the holiday flights will vary by season, but most will not run over the winter.
To operate a regular, frequent bus service will not be commercially viable because a particular trip may only be busy one day of the week (and possibly be a fresh-air express for the entire winter). We're not talking about Heathrow, Gatwick or Manchester where there's flights taking off or landing every few minutes. Even Bristol has over 10 times the passenger count of Bournemouth.
Arrivals are harder to judge because of flight delays - a flight could be on time one week, and six hours late the next. Again, a bus could be busy one day, but carry nobody the next because the flight is suffering a five hour delay. This is much harder with later arrivals, as Bournemouth's runway closes overnight, so anything landing after 21:30 gets diverted (unless they can get air traffic control to stay later), usually to Gatwick or even Birmingham.
As the airport is much smaller, there's a smaller staffing level, so again that affects any potential passenger levels. The existing service 737 is geared more towards the neighbouring business park - buses cater for shift times there as there is a much larger worker count there (even Amazon had a depot there until they moved to a larger site in Poole). The old A1 was an airport contract, the 737 being introduced by Yellows on a much pared-back timetable after the funding was pulled (why pay for a bus service when those passengers could come by car or taxi, so the airport gets more money from drop-off fees?). It is also why the 737 was sent via the suburbs - benefits more of those workers at the business park.
As for trams, momorails and whatever, if a bus service couldn't pay, then there is no chance any other mode of transport would do better! Not on the low number of flights Bournemouth sees each day. There would need to be a substantial increase in flights (and passengers willing to travel to the airport) to make a more frequent bus service pay. Southampton's proximity means load is split (and that airport has the advantage of a railway station). Additionally, Heathrow is only 90 minutes away, Gatwick and Bristol a further 30 minutes each - the concentration of airports in the south is also disadvantageous for a small airport.
Admittedly, there are plans to extend the terminal building to cater for Jet2's schedule - that could release Section 106 funding that would pay for a bus service (as the owners would have to use that on external infrastructure improvements!).