Yes, the Cadillac Mountain Southwest Trail actually begins along one of the roads that loop through the campground. If you can't locate it, walk out to the entrance of the campground and just across the road to the left is a trail head sign - usually a number of cars are packed in that area of people hiking the trail.
The Cadillac Mountain Southwest trail crosses the Bear Brook Trail just beyond the Featherbed, a small mountain pond. From there is climbs to the summit of Cadillac Mountain. Once there you really have two choices, either hike back down the way you came, or hike down the Cadillac Mountain North Ridge Trail and catch the free Island Explorer bus and go to the Bar Harbor Village Green, where you can catch the Sand Beach Bus back to the Campground.