The western end of Section B is near the Angler's parking lot. (Go left briefly on the towpath to reach the trailhead.) Billy Goat B is 1.4 miles, plus a mile to get back to where you started via the towpath. The rock scrambling isn't as constant or extreme as on Section A, but there are some scrambles, so wear appropriate shoes. You may also want to take a copy of the Park Service map.
From the Angler's end of the trail, you'll have an easy walk of about a half mile through the woods to get to your first view of the Potomac. You'll see the cliffs of Offutt Island: in the 1700's, the Offutt family owned this area (and much of what is now Washington, DC). The island was anonymously donated to the Nature Conservancy in 2007.
As you start following the Potomac, you'll notice the trail is much rockier. Soon, though, you'll break away from the river views and the rocks to follow a stream inland briefly, before crossing it. The last time I hiked the trail, I came across two deer browsing along the banks here as I was crossing the rocks.
The trail heads back to the Potomac for more open, rocky scrambles and more island views, interspersed with sections of woods dotted with enormous boulders.
If you follow the blue blazes, you'll eventually curve off to the left, following the small piece of the river that's channeled between the mainland and Herzog and Vaso Islands. Up a set of stone steps and you'll be back at the towpath.
From here, it's an uneventful mile along the towpath back to Angler's. Or, to keep going, Billy Goat C is less than half a mile to the east. Extra bonus: as of September, at least, there was a beaver dam in the section of the canal between B and C.
Last week: Billy Goat A
Next week: Billy Goat C