The x5 service passes through Bicester. You could consider extending Sonic's idea by buying a ticket to Bicester Town and catching the Megabus from there if you want to make the most of trains without touching London.
Please note that i suggested the megabus site, because the cheap fares are only available Cambridge - Oxford. Normal fares apply for any other Destinations. The X5 is actually operated by Stagecoach in Bedford.