I used several different 9V adapters from other gear - nor really paid any attention to the brand though some were Boss, and they all worked fine on the BB. I’ve since converted to batt power and no longer use adapters.
I do a lot of busking (street performing) so I need battery-powered gear. I made a small pedal board, approx 20" x 12" and mounted my BB, the BB external switch, my TC helicon vocal harmonizer, a 12V 4.5AH battery and a 9v converter. The TC requires 12v, the BB, 9v. The converter is smaller than a book of matches. The system will play for around 4 hours with the 4.5AH battery, which is normally sufficient. A 7AH battery will fit on the board but I haven’t needed that much capacity.