I have done both. I have GMed a multi-session one-on-one game and co-GM’ed regular sessions. BW works great for both. For one-on-one play it is simply the best option there is.
What you are doing is more similar to GMless play. I would worry that because both of you have skin in the game-- tensions can arise from setting difficulty numbers and arbitrating consequences.
I would suggest that before game starts you divide responsibility of the main setting elements. That person will have the final veto or say in matters of contention. Setting elements are things like “High court politics” or “Magical powers”.
One-on-one play can be very intense. Plan for shorter sessions, but expect very sharp conflicts. Mechanically, because of how obstacles are figured in BW, I reccomend playing characters with well developed relationships or access of Circles. Dice from help will be instrumental for survival. And, will also help populate the setting.