I agree that you can stay in Bayonne to see the whole area; no need to change hotels. There are local buses frequently between Bayonne and Biarritz.
While Biarritz has few "sights," I enjoyed it more than Rick did (we all know how allergic he is to visible displays of money). Where else can you see a surf shop next to an Hermes store?
I wasn't on the tour, but agreed with the statement that used to be in the pre-tour info (not there any more, for some reason): "If you arrive a day or two early, note that we'll be visiting all of Bayonne's major sights as a group." Bayonne only has about 40,000 people; it's much smaller than the designation "city" would imply, and doesn't take long to "see."
So, planning to get there a day early and using that day to explore Biarritz, is a good idea.
As for transit for the tour, yes it is tricky. Both Biarritz and Bilbao have airports, but not as many connections from these to the US as one would like. You may want to get to Paris at the beginning, and/or Madrid at the end, and take trains from these points to and from your tour.