I am an entrepreneur in SF who is interested in assembling a board of directors. What is the best way to recruit experts who will genuinely be interested in mentoring and working with your company?
I think the premise of your question is wrong. The best way to recruit experts that are most likely to be helpful is not by building a Board of Directors.
Being on a board has a tremendous set of responsibilities that most people aren't prepared to take-on initially.
Furthermore, most early-stage investors believe that a working board is "overkill" for companies that haven't raised at least $1m in seed funding, so you might be exposing yourself to negative signal by actively building a board.
Given that you live in SF, you probably have already experienced the tremendous spirit of helpfulness that exists throughout SF and the Valley. If you are able to get through to people you consider a potentially good mentor, you'll most always be able to get at least a 30 minute coffee.
If there's strong personal chemistry between yourself and a mentor, they might be willing to formalize an advisory relationship where in exchange for equity, they might agree to do more work for you including making introductions.
But I'd be very cautious about formalizing a board relationship with anyone at this early stage.
I find LinkedIn and AngelList to be very powerful when combined. AngelList can be used to find people who are actively investing and advising, and LinkedIn is a better means of cold contact if you make your request contextually relevant.
Happy to talk to you in a quick call to share more of what I've learned in recruiting great advisers and investors.