Changing a barrel on a Savage/Stevens boltrifle takes all of ten minutes if you have the tools and any mechanical ability. Not so long ago Savage didn't make a short action, they used the long action for all rounds. My 22-250 is a long action. You will need a mag box filler, your new barrel, a no-go guage for .243/.308, a barrel nut wrench and a large vise with wooden blocks.
Depending on what barrel you bought it can be done for somewhere between $150 and $500.