If our dogs got covered in mud or slobbered on in the dog park, we just rinse them off if at all possible; when shampoo is needed we've had luck with an all-natural oatmeal shampoo that is designed for both cats and dogs (an absolute necessity, if you ask me, because of the way our Bs groom themselves; only-ok-for-dogs shampoo will likely have things we don't want them ingesting). Our dogs sleep in our bed with us, so we're pretty sensitive to their level of cleanliness. Even at that, they need an actual bath in the range of once every 3-4 months. Every 4-5 weeks is WAY TOO often for basenjis.
One of our Bs tends towards dry skin, too, so we give her the occasional spoonful of coconut oil to EAT, or even a pat of butter. In our experience, ingesting a bit of fat does wonders for her skin dryness; adding anything to the outside doesn't work for us. Healthy fats, depending on what she's willing to eat, should help a lot.