An original equipment part would be about $200. Labor should be an hour or so.

I don't think a reputable or competent mechanic would work on a car without him/herself independently verifying the customer's complaint. In this case it means re-reading the codes to see if the same one is present and/or if new ones might have appeared. This is easy to do and wouldn't with an honest shop incur an extra charge if they were going to go ahead and do the job.

This is not a specialized repair and a dealer would provide no advantage. The only issue is as the other post suggests, being sure the correct oxygen sensor is used. Use of the wrong one can be a problem especially if your state or town has emission testing.

There can be various reasons for an oxygen sensor code even if sensor is not bad, such as vacuum leaks - see posts from Klaus. If your car has any performance deficits or poor driveability symptoms, tell the mechanic about them.