I think my up-to-eight-at-a-time-over-39-years pack have had less than 10 baths between them all !
Stop the baths, instantly. Why bath a self-cleaning animal like a Basenji ?
My penultimate pair, Hoover, and Keepurr until he died in July, went to the woods to run free daily. They were often extremely muddy when they jumped back into the car for the trip home. 12 minutes and 8 miles later, two pristine Basenjis emerged. Now Hoover is on her own, winter and mud are upon us with a vengeance. She gets very mucky, but arrives home clean.
My dogs have always had a small piece of lard - genuine lard (bacon dripping) not the sunflower oil stuff because they need the animal protein - daily to keep the skin and fur flexible and glossy. Just a small piece on the end of the knife. Not enough to make them fat.
Basenjis love to be groomed. Almost as much as they hate to be bathed. Get a male hair cream preparation, I use Vitapointe. Squeeze about an inch onto your hands and rub them lightly together. Then massage the cream into the dog's coat very thoroughly. Leave for a few minutes and brush it out - dogs will love the attention and coats will gleam.