I have a Facebook Business Page and want to limit the users and fans to those approved by the admin.
I want my fans on my business page to be a more exclusive group than anyone who comes across it.
Is there any way to do that?
There is no way to prevent someone from clicking the "Like" button on a Facebook page, and there is no way to prevent people from commenting on posts to your Page.
If someone does comment on your Page you can click the X to the right of their post and choose "Delete and Ban User". But you'd have to constantly watch the page to do that for every comment that comes in-- and that's not manually feasible.
Here's a way you could achieve something like what you describe:
NOTE: In the answer above I don't link to example companies or services, because as a new StackExchange user I can't post more than two URLs in an answer. Sorry about that.