There is no corresponding student level classifications for bonsai as there are in the Japanese martial arts and other old trades. From what I understand, that "iemoto" system that used accepted forms to evaluate whether an individual practitioner has mastered them sufficiently intentionally wasn't used in Japan for bonsai. Modern bonsai relied more on the Western exhibition/competition to advance the hobby/art.
This article on the Japan Policy forum written by a former Omiya Bonsai Museum curator provides some keen insight on this topic.
The Ōmiya Bonsai Art Museum, Saitama, opened on March 28 in Saitama City, not far from Tokyo. It is the first publicly run institution in Japan dedicated to the art of bonsai. The museum is located in an exclusive residential area known as the Ōmiya Bonsai Village. The Bonsai Village developed...
www.japanpolicyforum.jp
this passage from it in particular:
"The history of Japanese bonsai as it exists today is actually quite short, going back just 200 years or so. As is well known, one of the characteristics of many of Japan’s traditional arts is the iemoto system, by which the traditions of a particular school are handed down from generation to generation via a formalized and often hereditary hierarchy. Bonsai is different. Although it is often grouped together with the other “traditional arts,” bonsai does not really have any strict “schools” or an iemoto system. The reason for this is clear enough given the historical development of the art as I have just described it. For art forms like the tea ceremony and ikebana, and traditional performing arts like nō and kabuki, the framework of the art forms as we know them today was in place by the end of the sixteenth century at the latest. Once an art form has come to maturity, a certain amount of time is required for the various schools and the iemoto system that controls them to form. But in the case of bonsai the modern age, spurning “schools” and the iemoto system as feudalistic, arrived before sufficient time had passed for the system to be fixed in place."
"Unlike other traditional arts, bonsai has never developed well-defined schools or an iemoto system to transmit the accepted forms and evaluate whether an individual practitioner has mastered them sufficiently. What takes its place in the world of bonsai is the modern social phenomenon of the exhibition, imported from the West in the Meiji era. It is by continually holding exhibitions that bonsai has found a way of transmitting the forms and evaluating skills, and of assessing the creativity of a practitioner as expressed in the way he or she uses those forms. It has therefore succeeded in performing its role as a “traditional art.” The best-known exhibition of all is the annual Kokufū Bonsai Exhibition, first held in 1927. As can be seen all too readily from the appearance of its cities, modern Japan has consistently preferred repeated cycles of destruction and rebuilding to a sustained effort to maintain the old. Within this cultural context, the art of bonsai, nearly two hundred years after it began, and with an exhibition itself already more than 80 years old, has managed to carve out an impressive tradition indeed."
So, if you're looking for an "official" title of what a bonsai student is called, you're out of luck. I've seen Japanese hobbyists post here as "bonsai ka"