001,
Stn Cdr's discretion comes down to just that. Fine taste and good judgement. These things by definition attract attention. If OC RAF XXX has his name or his station on the front page on a regular basis his AOC is going to start asking questions. Nobody is free from supervision!
Costs are a strange animal. What is the extra cost of flying a pax? In a twin crew aircraft, the navigator looses out on some flying time. In a twin seat version of a single seat fleet there is possible a little less flight time due to less starting fuel. The pilot has to fly to stay current, the jet was going to fly anyway. Its all already in the budget use it or loose it! There is good training value (experience) for the pilot in looking after someone who is totally new to the environment. Taking up a pax is not a no-brainer. I took a pax in a Hunter once who grabbed hold of my arm at the first turn after take off and took some convincing that he wasn't going to fall out! I bore the finger imprints for days.
The pax has to be approved, there is a medical required and the insurance bods get involved, the guy gets fitted out in flying kit that get laundered after he flies (cost a few quid). He then needs to have egress/ejection/survival instruction, some distraction of manpower required to do this but there is no overtime in the forces.
The judgement required by those approving the flight is "how will this be viewed by the outside world" what other deserving cases are there out there from within the service. Air trafficers are a good example of good cases for a famil ride. A 'well done' reward for a hard working individual, long service recognition even a compasionate return home trips have all happened. SMO, SEngO, OC Admin (when he has the impress (imprest) money on a ranger)
In the Hawk world it was easy, a lot of spare back seats come up when there are instructors in formation leads with a solo student on the wing (pax flies with instructor not student). It becomes a bit more of a burden if there are certain things the pax "has" to do in the likes of a Tornado. In any "trainer" which can be flown solo its a far easier case.
If you are asking "what do I need to do to get a trip" (assuming you are not currently serving) then the easiest way is to get into the TA or RAF(VR) and write to the station. Otherwise become a local dignitary, chief of police, chief of fire brigade. Maybe even become a sports star or pop star (I flew Gary Numan years ago).
Hope this helps
Tarnished