[Scorch]

Try a very tight patch from the muzzle end first. When it gets to the neck area it will probably pop the case out of the chamber. If that does not work, plug the bore with a patch right at the front of the chamber, pour a small amount of melted CerroSafe or melted lead into the chamber, let it cool, then knock the case out of the chamber with a cleaning rod.

For a bolt action rifle, if you have neither of the items described, you can remove the bolt, mix up some epoxy, put a smear of it on the corners of a 1/2" dowel, and carefully put the dowel into the broken case from the breech. After the epoxy cures, just pull the broken case out.

The first two methods will take about 5 minutes to try. The second will take about 1/2 hour because of the cure time. In your case, either is faster than driving to the gunsmith. Good luck!