I did this journey every day for 3 years!

It really does so come down to where in Oxford they are going to and
where in London exactly they are coming from. Being in Paddington means
(I think!) that you are not that handy for either main bus service
(Oxford Tube and X90). The bus from central London to the Headington
roundabout takes 90 mins (prob another 10 mins in to Oxford at least)
and IMHO is not viable: furthermore the cost is high if a travelcard is
also needed. As for bus lanes: there are some and they do help, but in
the run in to Thornhill P&R, you will still be sitting on the bus for
up to 20 mins very regularly.

The train is good but expensive: it was always pleasantly quiet but a
little prone to delay.

I drove most days: without speeding, you can get to Headington
roundabout from, say, the Wooloworths building on Marylebone Road in
just under 50 mins (leaving at 7:30am - more and more the later you
leave it). Again, it's pricey: reckon on about £12 a day in petrol. I
spent £9 but that was 2 years ago and with a 1 Litre Micra.