I started playing hockey when I was 4 years old. I could barely skate, the puck felt like a lead weight, and if I took my stick off the ice to wind up for a shot I would fall down. But I was a hockey player. You don't need to be a Gretzky or a Crosby to be hockey player. You don't need to play in a certain league, you don't need to be any good, and you certainly don't need the approval of a bunch of guys on the internet. The kids just learning, the old guys in the local beer league, and the professionals in the NHL are all hockey players. If you play hockey, you are a hockey player.
Its the same for bowyery. If you make bows, you are a bowyer.
Now that I think about it, the only requirement that I see is that you kind of need to be doing it on a regular basis. You can't make one bow, one time, never do it again, and still call yourself a bowyer. But if you've got a couple under your belt, and you are continuing to build and learn then I would say you are a bowyer.
Now lets remember that just because you are a bowyer doesn't mean you are any good at. I think some guys have attached an almost mystical meaning the word, setting standards that most people will never reach.