Totally with eeefarm. If your dog bites, especially if he breaks the skin, you could wind up in a world of legal issues.
First, get a muzzle and if you have to take him around people, use it.
Second, the very first nip should have resulted in immediate training ... one critical command is down, then stay. Once in position, you can simply put you foot on the leash. If the nipping is frustration, expect to be the target. Dogs that bite WILL bite anyone they feel needs a correction. You can now use a stern "no bite!" and ignore.
Fourth, I am always on my own on this...but I'm 62, have had Chows most of my life, bred & trained Rottweilers, and worked on rehab and aggression with private but mostly rescue dogs of a dozen plus breeds. While I owned only 3 Basenjis, I doubt my 3 are that different than other basenjis. While all breeds have a few quirks ...such as basenjis reacting to "ouch " like a squeaky toy, they aren't that different.
Personally, I lump them generally in the "obedience, rules, bah humbug. What's in it for me" group. I find the need to make the dog believe it is their idea or find the right response is very common with ancient breeds. You can be the judge of what level of craziness is shown by my owning 3 of them (chows, basenjis and samoyeds).
So, no basenji-familiar trainers? Find one that is willing to learn. They still need the basic skills. If the trainer indicates your input is worthless, get another one. Trainers train owners, not dogs. You have to be able to trust and communicate.
Fifth, biting can't be evaluated or fixed on the internet, as indicated above. We can give general suggestions. So I'll suggest a few safe ones.
Start obedience from the beginning. You need to seriously address who is in charge. But the bed is an issue only if the dog guards it.
Enlist help from people to come near so you get a lot of practice with down-stay. Eventually he will learn that you decide when to move on, and that he will get a lot of praise and a treat if he's quiet when you are ready to go.
I have some good links but no access. Fell and am confined to my recliner for a couple of more weeks. Using a kindle is frustrating.