I hear you about the long drive..........it sucks to drive too far now with the gas prices what they are. I live close to CF so its easy for me to run up there anytime, and it is a good place to go for bears; I'm just saying that it gets hunted hard now during the spring because of the special permits for damage control.
There are still a bunch of bear up in CF and a good place to try, but if you also are going to be scouting for elk hunting areas while bear hunting then you may want to look in other areas. There are a few elk in CF but they are hard to find. If I were you, I'd look for bear and elk south of Alder Lake in the Gifford Pinchot National Forest. It is within an hour drive from Ft Lewis. Just take Mountain Hwy (SR7) south out of Spanaway toward Morton. You'll go through La Grande, Alder, and Elbe. SW of Elbe there are a bunch of Forest Service roads that you could drive to scout for elk and look for bear.
Hope that helps a little.
Welcome to the site and welcome to Washington State.