Not an authority myself, but I always viewed Bushido as the "Do" or way/path of the "Bushi" - Warrior of the Japanese samurai class (of which there were other occupations) during the warring times in particular.
Budo on the other hand is Martial "Bu" Way "Do", meaning the study of war and war arts as a path/way, leading to self cultivation etc.
To me, the Bushi/Bugei were a particular social class of people existent during the Tokugawa and warring states period of Japanese history and as such, their "Do" no longer exists as the system/societal reality in which they operated no longer exists (i.e. there are no more living Bushi in Japan from the 19th Century who follow the code as it was intended). Their descendents, though of Samurai family heritage, are still not Bushi, since this particular social entity (i.e. warriors and retainers in service of a Shogun/Lord) is no longer existent in Modern Japanese societal structure. Needless to say, I think that non-Japanese cannot consider themselves as Bushi in its literal sense, since this term applies to a particular element of an old traditional Japanese society that no longer exists.
Hence, I think today to say one follows Bushido may be oversimplifying what the term meant in its traditional sense, as there is no modern equivalent that exactly matches that time, cultural and societal reality, even in Japan. One can partake of the tradition and history and follow it figuratively, even incorporate some of its teachnigs into one's own Budo training/living; but the Bushido code was strictly intended to be limited to the Bushi (warriors of the samurai class) and no one else imho.
Of course I can be wrong, but from what I've read and understand of the history, this is what I have gathered.