If a bisexual man marries a man, and doesn't divorce, but moves to California...

[Boojatta]

... then could he woo a woman in California, get engaged to her, and go through the least expensive procedure to officially get married to her without running into any legal trouble in California?

I'm wondering because there has been a legal issue involving bigamy and members of splinter sects of Mormonism. In those cases, there are typically accusations of bigamy even when there is only one official marriage, along with some unofficial religious ceremonies.