How does everyone use twitter to meet providers? I have found a couple of ladies who provide and I can follow them, but I cannot figure how to contact them if they are not following me on twitter.

In their profile or bio, they should provide a link or way to get in touch with them...
..or you can post a tweet, or reply to one of their tweets and ask them how you an contact them privately.

Unfortunately with Twitter, someone must be following you to be able to send them a private message.

It's really simple. Unless they have blocked you. You post mention them like this @Cinnamongfe and your message and they will receive it. Unless they follow you, you can not DM (direct message) them.
Feel free to follow me, I always follow back.
It's a great marketing tool. IMO
Good luck
xox