The Ritz is one of the best places I have ever stayed, but I'm sure the Four Seasons is fine as well. Bachelor Gulch is a 5-minute shuttle bus trip over to Beaver Creek--it is not in Beaver Creek Village itself. So there is not much to do at Bachelor Gulch itself, but that may be more to your liking anyway. The Ritz has a nice pool area by the Bachelor Gulch ski lift.
Alternatively, your wife may appreciate being in Vail more than being in the BC area, which may be the top consideration for you. Vail Village and BC Village are about 15 minutes apart by car, IIRC. BC has some world-class restaurants, while Vail's restaurants are good, but not quite as good. You can also get some decent meals in nearby Edwards and Avon if you don't want to have fine dining every night.