We've been doing some research to try to understand why, not only for suicide, but for other mental health outcomes as well, we see the same pattern where bisexual people have the poorest health outcomes. There does seem to be a major role for discrimination and associated lack of social support.
Many bisexual people are isolated in terms of lacking a community of support from other bisexual people. Many bisexual people face discrimination, not only from heterosexuals but also from gay and lesbian people, and so may not feel that they have a welcoming source of support within the broader lesbian and gay community. As a result of that, many are quite isolated with respect to their sexual orientation, and they lack support in that way.
Also, the data suggest that in terms of economic disparities, bisexual people also fare the poorest relative to other sexual orientation groups, so it's also very likely that the economic stresses that bisexual people are dealing with are also contributing to those mental health outcomes.