Facebook: Personal Page and Business Page

Make your personal account (you don't really have a personal 'page' -- the terms differ) private. Just jigger your settings (gear wheel, upper right corner of all FB pages. I can't give you specifics as FB is constantly changing this).

Then promote your business page, even by liking it as yourself or sharing its content on your own wall.

This is the kind of thing that a lot of rather individual sorts of 'business' owners have had to do, such as pastors with personal accounts to be in touch with family and friends who want church business handled through the church's 'business' page. Mid-level authors and actors run into this sort of an issue, too, and this seems to be the best way to handle it.