Heathrow to Oxford

I just went by bus from Heathrow Terminal 5 to Oxford last month and it was very easy. After exiting the terminal, the signs to the bus stop are very clear and it’s not far at all, it’s right out with the taxis.
I purchased from theairline.oxfordbus.co.uk
I didn’t know what time to purchase for so I chose 2.5 hours after I landed. I was at the bus stop an hour early, and they allowed me to take the earlier bus. They do take cash if you want to purchase in person, but take as close to exact change as you can.

The bus you want is called, strangely enough, The Airline. Runs regularly between LHR and Oxford. You can get it at Heathrow's Central Bus Station or a Terminal 5. It stops at various points in Oxford and ends up at the bus station which is close to the rail station there. We prepurchased tickets but I don't think we needed to, there were plenty of seats on our early PM departure.

As others have stated, the Airline is the best way. I've used it a couple of times and it has never been crowded. The coaches are very comfortable for a 90 minute trip and they depart frequently.

You can buy tickets in advance, but the price is the same if you buy it from the driver. If you buy in advance though, there is no need to worry about delayed flights, as stated on their website: For travel from the airport to Oxford, airline e-tickets may be used on any earlier or later equivalent service due to depart up to 24 hours before or after the service specified on the e-ticket.

Yes, take the Airline coach. Travelling by train will involve either travelling into Paddington by train and out again, or travelling by coach to Reading and then train.

Wow! I am so impressed with the replies I received. We will definitely take the bus. Thank you, everyone!