said 1 year, 4 months ago:
I think that people have different Facebook boundaries so it can be unwelcome to friend someone out of the blue. But the worst they can do is ignore you. I do know a lot of people who only use it for personal reasons but then those may not be the people who are liking your Page.
You could also try the reverse approach and ask people on your Page to come and friend you if they want to stay in touch which is what I think @stevencole was getting at.