I have very recently begun to see a neuropsychologist as I am having issues with depression, fatigue etc. Is it appropriate to ask his sexual orientation? This is somewhat important to me because much of my frustration and anxiety are related to the fact that I am a bisexual married man living in a very rural community, unable to tell anyone of my illness.

You are to be commended for addressing your depression and fatigue, as these will have a direct impact on your physical health. A high level of comfort with your neuropsychologist (or any health provider) better enables you to share very personal information which is necessary to benefit from therapy. Rather than directly asking about his sexual orientation, I would suggest inquiring about his knowledge of bisexual issues so that you can be assured of his competence and ability to help you with these concerns. Your therapist can become a central part of your support system, which is especially critical given your rural location. Don't forget that there are online resources that allow you to give and receive support via the internet.