According to Azhandar in the Loremaster's Archive - The Arcanists, Arcanists have to be chosen by their books, and they need their books in order to cast Arcanist magics.
How does Bahtra at-Hunding get people subclassing into Arcanist skills their books? Does she have a deal with Hermaus Mora that allows her to give some out? Maybe she unlocks people's potential and that makes them palatable for an arcanist book to manifest on Nirn and choose the subclassed adventurer? It is not explained.