You won't get a mooring in the centre of Cambridge I'm afraid- there's a waiting list which is currently closed.
CCing is possible but bloody hard work, because all the moorings are 48 hours so you're moving every other day. There are visitor moorings to commute to Cambridge by public transport at Cambridge Jesus Lock, Waterbeach, GOBA at Bottisham Lock, Upware (with a cycle ride), Stretham, Little Thetford, Ely, Littleport, and Downham Market. Moorings out towards Bedford are also commutable- St Ives right through to Huntingdon is served by the guided bus, then Huntingdon to Bedford by the X5 coach. Having a car probably won't help unless there's two of you.
CCing means moving between one and three hours every other day, after work in the evenings. I wouldn't recommend it.
The Cam Conservators are the licencing authority for the Cam above Bottisham Lock, you can pay a small supplement to your EA licence to gain access for up to 90 days in a year. Buying a CamCon licence gives access to the EA Anglian region too, so not just the 9 miles.
If I were in your situation, I'd look at mooring in:
-Shrubb's Wharf
-Tiptree marina
-fish and Duck marina
-Moorings at Stretham
-Upware marina (and the small moorings on the end of the Lode)
-Cathedral at Ely
-Little Ouse
Or possibly Jones in St Ives. All are commutable by car, but will involve either the A10 or A14 which gets busy. Anything further away than Little Ouse will be a nightmare commute- Ely can be hard enough.
The other alternative is somewhere at the top of the Lea or the Stort, and driving up- in my opinion much better boating, and possibly less traffic up the M11 into Cambridge that way.