Well, I just got a bassoon and I noticed that the corks on the tenor and long joint are coming off and I was just wondering where I should go to get them re-corked and how often I should do so.

re-corking tenons is quite a straightforward job - any woodwind repairer will be able to do them. Nip into your local music shop, if they don't have a repairer associated with them they are sure to have a list of local people.

As to how often - not very. Only if either the cork is falling off or isn't making a good seal anymore and the joint is wobbly.