I've been to Big Bend many times. I've stayed in several different campgrounds. None of them are what you might call a resort.
I've spent the most time at Big Bend Resort and Adventures. This is a desert campground 3 miles from the west gate of the national park, in Study Butte, TX. I like it here because they have gas, grocery shopping, nearby restaurants, and a store. This is where I'll stay next time I go.
Mavrick Ranch RV Park is in Lajitis, 20 miles from the west gate of the national park. It is a desert park too, but much of the lot is paved. They have most of the ammenities that you find in Study Butte but stuff tends to be more expensive (and everything down there is expensive). I stayed here once, but didn't like being so far from the national park activities.
Farther up the road is Marathon Motel and RV Park. This park is 40 miles from the main gate of the national park. I liked this park a lot. It is a desert park but it is well maintained. There is a big emphasis on sky watching here. There are a couple of really good restaurants in town too.
The park headquarters/visitors center is in the middle of the park. It is a long ways from any of the gates to the vistors center.
I wrote some report from my visits, complete with photos.
What activities are you thinking about?