I totally get the embarrassment factor: some little old lady with a cute little fluffy white dog is leaning in saying "oh, what a handsome dog, is she friendly?" And the handsome dog starts swearing and lunging at Fluffy. But I also kind of get where the dog is coming from, too. A few years ago, a Sheltie bit me on the calf – not terribly, not stitches-worthy, but out of the blue, and to be honest, I still think Shelties are demons now. When I see one, I don't swear and lunge but I do cross the street to avoid one. I'm still, well, afraid of them. Irrational, but there you have it.
So my advice, such as it is, won't really help your basenji; listen to other people for that :). My advice is really to you. Tell the little old lady. Tell the dog owners you meet. "She's still very afraid of other dogs because she got bitten last month." It really will help with the embarrassment factor. Explanation and communication in this kind of situation help us as much as it helps the people we are in contact with.