I acquired an older brother at age 35, he traced my mother who was also shocked, understandably, but although I knew nothing of him, my father and her parents knew about Andrew, and although initial contact was through letters, I now have regular contact with him and we are good friends. I would say that since your birth mother has given you a way to make contact, you should feel free to use it. You seem like a sensitive person and as long as you tread carefully, I cannot see anything bad coming of it. You will gain some closure and you may gain a lot more.
Be prepared for your birth mother not wanting to have a relationship - the past may be too painful, but the ball is definitely in your court.