DVLA leaflet INF52 (
this seems to be link to current version) is the most official source on this.
It says you can drive the following on class B (car licence)
a bus made more than 30 years before the date it is being driven, and not used for business purposes or for carrying more than 8 passengers
I had understood that driver also needed to be age 21+ but it does not say so there.
Note that all three conditions must apply, not one or two. I'm not quite sure whether a conductor (if it's a bus that needs one) in addition to the 8 passengers would be allowed. I'm not sure there has been a test case, but I don't want to be involved in it.
If you want to carry more passengers, even at a 'running day' type event where it is a genuinely free service and you are not being paid, you still need PCV entitlement (although I understand you don't need to have the driver CPC in those circumstances - this of course may have changed.)
I have seen it quoted on another forum (although the person stating it didn't come up with a source and I have not seen it in writing) that you also need to have D1 entitlement - this (in 'not for hire and reward' form) 'came with the rations' on a car licence up to about the mid 90s, but not since, and it doesn't automatically renew at age 70 unless you do the 'vocational' medical.
Some running day organisers are happy to have '8 seat' buses running, others find them an operational inconvenience and aren't. (it can be a bit awkward for a regulator to have to explain to a long queue that yes, this bus is full with 8 passengers.)
You would of course also have to be acceptable to the vehicle's insurers - some may not be keen on drivers with only car licences, but that's up to them.
Beware of information from random people on the internet / at rallies - the law has changed several times since the early 90s (before that, broadly speaking if the bus wasn't actually being used for hire and reward at that particular time, you were OK on a car licence) and there are people out there who remember bits of the law as it was not as it is.
And disclaimer that I'm not a lawyer or police officer or employee of the DVLA, DVSA or any similar body so my opinions aren't worth any more than anyone else's on the internet.
Also on a personal level, I'd strongly recommend getting some off-road experience and / or tuition from someone experienced (even if not a qualified PCV instructor) before taking a vintage bus on to the public roads.