The trail continues downhill from the top of the natural bridge to the bottom for one of the most speculator views in the area. I know some people will make the hike down for the sole purpose of seeing this view before returning to the trailhead. Still, there is more beauty to experience in the geological area, and I'd highly recommend continuing along the short loop across the cove.
Hikers can take the Natural Bridge loop in either direction, but I tend to take the trail at the far end of the arch. the trail wanders along the bluff and then gradually meanders a little further down into the cove to a stream. During wet periods this stream has some beautiful little cascade along with it, and if you look around, you may even find a salamander or crawdad. After crossing the stream, you will begin to climb a little toward another bluff line (this is the adjacent side of the cove that you came in on).
The trail will hug this bluff for a short time and take you past some incredible natural features. If you came in the way I usually do, then the first of these features is a crack in the bluff that you can walk through/behind that also has a smaller natural arch. This area is my second favorite part of the entire loop, and I usually take my time through here. There is a bench under the arch for anyone who wants to sit and take in the area's beauty.