If you are arriving BA you will arrive into T5 probably and then make your way over to T3 for Virgin Atlantic. The free bus will be airside, although you still need to pass through security again. You can also take Heathrow Express for free if landside.

IIRC you don't actually have to arrive in a car to access the Upper Class Wing. It is just a direct entrance from where the chauffeur drops you off. I suppose some people like being greeted by name, since they will be tracking the arrival of your VS limo. I doubt it is quite so seamless if arriving on private transportation.

However if you check in at the main desks, you'll be directed to a private lift taking you to the Upper Class security control which ought not to have queues. So not missing much really.