This website will answer your questions. https://www.abmc.gov/
From personal experience, you can get a bus to (near) the Verdun museum. But unless you're on a tour you're not going to get very close to any of the battle monuments. The "Verdun" battlefield is over 25 miles of front line that moved back and forth over 20 miles laterally. It takes days to see even a portion of it. I've spent over two weeks, over the past three years, visiting sites. I have taken a 5 day tour of the Marne focused on the American participation, but mostly I just drive. There are several excellent guides, I recommend the ones by Maarten Otte.
In Reims I use the 1919 Michelin Guide, which is very good for showing what the city looked like when the war ended and I find with a little work I can visit the places shown and described. The change is amazing. Reims is a couple hours drive from Verdun.
Belleau Wood is a bit tricky, it's behind the Cemetery outside Aisne. This is not reachable by bus that I know of, and I've never run into more than 2-3 people when I've visited. The path is marked, just go up the hill behind the memorial building. There's a German cemetery just outside the American one. The contrast is striking.
It's a 20-30 minute drive from there to the Chateau Thierry Monument, which sits on a hill overlooking the town. Great view from there. I think a bus gets you most of the way from town. Chateau Thierry is 3+ hours drive from Reims, straight down the champagne trail; it's a great drive, but not very fast because it cuts through a lot of small towns and the farm equipment is always on the road.