The written rules say you need 3 reviews to get onto the providers only board, but they also want you to have a posting history. Try posting more on your regional board or any of the general boards, for a month or so, then ask for admittance to the PO board again.

In the meantime, some providers may be willing to give you some advice via PM or email. As kk said there are screening methods that providers don't like to share on the public boards.

However there are many common methods that are well known as mrf and joe mentioned.
1) References from other providers
2) Memberships and "oks" from verification sites.
3) real names and work info
4) TER whitelists
5) google (names, board handles, phone numbers, email addresses)
6) blacklist sites
7) gut feelings

Most ladies will use one or more of the above. Every lady is different in how she screens, and what she accepts or feels comfortable with, and every hobbyist is different in what info he is willing to provide.

Figure out what works for you and don't compromise