Obviously, wet core is bad. I think, though, that it's easy to exaggerate the problem. If the core is bright, then it isn't rotted. Once balsa starts to rot, it will darken considerably.
How did you determine the moisture level? If you're using a moisture reading, there are a number of things that will artificially peg the meter, such as metal or interior bulkheads/furniture.
If the core is dry I would suspect the meter or, as IT folks say, it could be a U.S.E.R. error.
If the core is damp, then water is coming in from somewhere. As this is the hull, check through the through hulls and anywhere else water may ingress.
Once that's done, you can expose the core and dry it out. That can be as simple as tenting the area with plastic sheeting and aiming some heat lamps (at a safe distance) at the affected area. It will take some time so my advice would be to mitigate the problem, go sailing this season, and dry it out over next winter (if it really is wet).
Forget the vacuum bagging. It'll work, but it's expensive. For minor issues, tenting will work fine and for more serious core problems, vacuum bagging won't fix it (the core needs to be replaced).
[This message has been edited by Jason King (edited 04-17-2008).]