Rules are not posted on their website. I emailed them in October 2017 and finally heard back in January 2018, so don’t expect a speedy reply.
I have linked to their Rules and Camping Map (PDFs) in the links section below.
Dispersed camping is allowed within BTNF.
Pull off the road to camp. You may drive up to 300 feet from the road and camp in the vehicle there. You may camp further away if you leave your vehicle.
Time limit: 16 Days, after which you must move 5 road miles from your original campsite. You may return after an additional 7 days (23 days from when you set up camp).
Except in the Jackson Ranger District, where the time limit is 5 days. After 5 days, you must leave the Jackson Ranger District entirely, and not return for an additional 30 days.
No camping in Cache Creek or near ski areas.
Try not to camp within 200 feet of any water source.
Food Storage Order: Between March 1 and December 1, in most areas, all food and food-like smells must be contained within certified bear canistered, hung properly from a tree or pole, or secured within a hard-sided vehicle or trailer. No open-top vehicles, no pop-up trailers.
Catholes must be kept at least 200 feet from any water source. Pack out your TP.
I decided to tear out my van bed and kitchen and more-or-less start over. The insulation and paneling are good, so I’m leaving those.
You may recall the bed I had built previously (see below left). The weight was all on one side, it wasn’t anchored very well to the van structure, and we almost never collapsed it into bench mode even when driving. Furthermore, I chose the openable bench design because I wanted a hallway to get to the back door, but I never use it, which makes it pointless. Finally, in the event of a head-on collision, not much is keeping it from flying forward.