What a journey you've had, to finally being able to reconnect with your birth mother. I would imagine those moments just before you physically meet to be quite nerve-wracking.
As a genealogist, I've never had to try and track birth parents, but I do know there are now a great number of sites (like on FB) that specialise in helping adoptees try to track down their roots. It's wonderful.
My brother was adopted into our family, but he has never shown any interest in finding out about his birth parents. The genealogist part of me would be dying to find out!
I am glad for you that it has worked out happily. :)