I too was in your situation, as my hubpages will inform you. First of all Congratulations on finding your birth mother. For me this was both scary and exciting at the same time.
I started out by writing letters back and forth between my birthmother and myself. I was in the process of getting married and thought what better than to invite my birth mother to my wedding....That was scary....
Let me back track a minute. Growing up in my adoptive home,my adoptive mother always downplayed my birth mother. She would tell me she was overweight, uneducated, and a disgusting person. In my mind none of this could be true...after all she was my birth mom.
Growing through the pain of the abuse I lived with I held on to the thoughts that I would someday meet my birthmother and belong, once again to her.
So I did meet her and it was scary. She was in a wheel chair, as she had poor health. She wasnt of the middle to upper class, but I didn't care. Sitting there was the woman who once made a difficult decision to give me up because she thought it was best.
In hindsite it was better for me...even though I had to go through the abuse.
Communicate by letters, and when you feel up to it get together and go to dinner, a movie, or anything the two of you enjoy.
I eventually lost communication with my birth mother on my own decision as she would repeatedly make me feel bad that she couldnt pay her bills. Almost asking for money.
When I did decide to get back into contact with her, I instead found her obituary on the internet. I contacted my birth brother whom I had also communicated with off and on and he verified it was our birth mother.
I can't guarantee things will work out like you had pictured in your mind, as they dont in most cases. But if it is that bond of knowing your biological mother, keep the lines of communication open and the relationship will develop on its own. Remember at one point in time she did what she thought was best for you. No one can predict the future for their child when choosing adoption, they are choosing for that moment in time.
Best of luck to you!!