I'm betting you will need at least 1K for the re-barrel on an A-bolt. Most gunsmiths pricing I've seen is about $650-700 for a new barrel if they provide it and your action gets the full treatment, like square the receiver, polish the action, and lap the lugs. If you provide the barrel it is quiet a bit cheaper but then you pay ala-carte for everything.
zoomie touched on most of the stuff. Bushing up your bolt face to accept a smaller rim diameter is a lot of unecessary work when there are plenty of cheaper actions to work on. Plus you will need to change out the magazine because again the larger mag probably won't hold in the 6.5X55 cartridge.
If you don't want to do a .260 Rem on a Savage action which would be your cheapest route with a new rifle and basicly the same performance as the 6.5x55. You can always try to pick up a used rifle like this one Husqvarna 64B
. Then it might be hit or miss about the accuracy of the rifle.