Was watching Raising Hope in the episode where new owners have bought the grocery store and when they are washing the dog, on the floor there is a red and white Basenji just sitting there for a few seconds. Pretty random.
I applaud you for getting a rescue. There are tooooo many out there. For a first timer, an older one would be good, at least 18mos old or more where their personality is who they are at this age. Research all you can, and if you fill out an application and are denied, no not stop trying. I was denied by a Basenji rescue, and Uzie is my second where I found him right here 'free to good home' so we drove two days to pick him up and he is thriving without fenced in yards. (not for everyone as not everyone lives on 10 acres or more…I get this....!) but he has blossomed and doing well. So, don't give up!
I have a friend who swears by her Walkydog, takes her basenji for 6-8 mile rides when it is cooler. It evidently unclips easily if your dog needs a pit-stop. I'm afraid any one of my 3 would drag me to my death if attached to me on a bike.