Lukas' answer cover Enterprise Distribution pretty well, so I'll outline the option of general release, restricted user base.
Firstly I'd like to point out, it seems Apple is of the mind that beta versions shouldn't be allowed, for example in the Apple Store Review Guidelines (login required) it states:
2.9 Apps that are "beta", "demo", "trial", or "test" versions will be rejected
That being said, I've seen a few apps which are beta versions released on the store, so this rule may be a bit more lax than some of the others.
I'd consider releasing the app on the normal app store following the same pattern as any other application with a few changes:
- Phrasing: For Apple's benefit, you're releasing a full app, not a beta, it's the users that are restricted, not the app's features.
- Add a login form to the front of the app to allow only specific users to use the app.
- Add the ability to create a beta account. (And limit the number of users as you see fit)
- Consider releasing the app in a limited number of countries to get an idea of your user base without exposing your entire market to a potentially flawed app.