My policy is coming up for renewal and I had 9 years no claims. In Dec 08 I had a bump, not my fault. On my statement of information it says under claims and convictions details "Accident – no fault – cost recovered by insurer". Presumably, this info is available to all insurers.

ok, so when shopping around online, what do I put when it asks you questions like "how many years no claims", or "have you made any claims in the last 5 years". Often they are just yes/no answers or drop down boxes with 1-9 or something. Presumably, these are questions which can massively influence the resulting quote.

What's the best thing to do? Does the fact that my costs were fully recovered mean that I actually haven't made a claim?

Your NCB and your claims history are farcically totally unrelated. If you tick yes to the claims in the last 5 years (and you must, and that info is shared between insurers), you will be asked to explain what sort. I have found that non-faults make no difference to your insurance. Most insurers dont recognise beyond 5 years NCB anyway, be wary to get notice that you have your full NC period, not just the 5 the last insurer wil consider its max.