I have been down the B Chain at least 6 times over the years.
We usually break the paddle from French to Olifaunt into 2 days because we have done the trip mostly with kids.
We always camp on Bud lake. There are at least 4 sites to pick from, not all of them prime, but all usable.
There is one right below the portage from Beg on the west shore looking at the pool below the rapids. There is one on the east shore in the narrow part of the north end of the lake. The one we camp at is on the south side of the 3rd Island coming from the north. It is open, sloping rock with a decent flat spot. Most people take the north channel so not much traffic. Good walleye fishing in the current on either side of the island. 4th site is on the middle of the larger island out from the portage to Fern. Decent spot as well. Nice sound effects being near the rapids to Fern. We have caught quite a few bass and northerns in Bud as well as the afore mentioned walleyes. There is an eagle nest across from "our" site as well. In 2008 it had 2 young ones in it. Let me know if you want more info.
Have fun.
Gene M