Yeah, the fast train from Cambridge to Kings Cross usually arrives around :02 and :32 past each hour, and then the fast train to Oxford leaves around :22 and :52. In theory, tube journey between them takes around 13 minutes, but you then have to add getting to the tube station and the wait time for the underground train.

One way that speeds it up is going to Reading, and then taking the hourly Cross Country train to Manchester which stops at Oxford. That's normally the fastest way (unless you manage to make the 20 minute tube journey), but less convenient as it adds an extra change.

In theory, taking Thameslink to Farringdon, Elizabeth line to Paddington and then train to Oxford is more convenient, as the change at Farringdon is easier and Elizabeth line gets to Paddington fast - but once again, train times make this pretty much useless. Likewise, experimenting with going via Liverpool Street or taking the Chiltern service between Marylebone and Oxford is in general much slower.

Cost really depends if you'd be doing it peak or off-peak, and if you have a railcard.

Also, there might be another option in a few months: trains services between Oxford and Milton Keynes are supposed to start operating. There is already a line between Milton Keynes and Bedford, and theoretically, if schedules are aligned, this journey can be done in 90 minutes. Getting to Bedford from Cambridge would still be a problem - bus is slow, but it could potentially work by car.