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:
Create a closed Facebook Group for your business. This is in addition to your Page.
Create a Custom Tab. You may need to use a third-party service to do this, unless you are fairly technical. Examples of companies that provide these services include
Make that tab the default landing tab for your Facebook Page.
On that tab, you can create a form (I know that Vitrue offers this, don't know about Short Stack offhand) for people to apply to become a member of your Facebook Group.
Examine the submissions of the form and invite those you approve of to become members of the group.
In the meantime, you should be posting to your Page to the rest of your fans, but reserving the special content for the members of your closed group.
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.