There are no "regulations" when it comes to apprenticeships in America. I don't think there are any in Japan, for that matter. It takes a will and a way. You can't just sign up to become an official apprentice, although taking courses with local bonsai experts (Bjorn, Michael Hagedorn, Ryan Neal, Bill Valavanis and other U.S. bonsai professionals) is probably a good way to start. Those contacts can also introduce you to contacts in Japan. Many started their bonsai careers with professional introductions from U.S. bonsai experts to bonsai nursery owners in Japan. I know Ryan Neal kept writing one such nursery a letter a month for years. He began as a teenager I think...He got an introduction to the Japanese professional (Kimura) and that led to his apprenticeship in Japan with Kimura.
Here's the story-worth a listen:
the story behind ryan neil“Mirai” is a Japanese word referring to the future, or more specifically, a future which has yet to be realized. In this short film, we follow bonsai professional Ryan Neil as he describes his journey to becoming one of the most recognized names in the American Bonsai...
bonsaimirai.com