Do you know your birth mothers maiden name/dob ? If so, she could be quite easy to trace, with contact with the correct people.
There are avenues you can do down to track her down, i wouldn't even bother telling the adoptive parents, this is your mother and you want answers/to meet her, they can't stop you.
I was adopted too, i tried to find birth mother in my teens, i tried everything, i first went to the social services (UK), they gave me a birth record of her details (name/dob/siblings/what she looked like) and details of her situation leading up to me being adopted, all on 3 sheets of paper.
They then went onto tracing her, i got called back a few weeks later, they said the council house she lived in, she'd moved out of it two weeks prior with no forwarding address, and as she didnt move into another council address, the trace was now lost...id missed her by two weeks.
Fast forward a few years, i had a fake facebook account (no pics or nothing), one evening i decided to randomly start typing her name in again, but i did it differently this time, and typed her name and her location, remember i had her name/s from the birth data i got. She came up, but i wasn't sure it was her as i didnt know what she looked like, as i started looking through her friends/pics, then i started to join dots...it was her, turned out i also had a real sister and half sister too.
I then a couple weeks later plucked up the courage to pm my real sister on facebook, and explained who i was.
My sister then came to my city the following week to pick me up to take me to meet "the mother", .....anyway to cut a long story short, i went down 3 times to see her in total, but it wasn't no happily ever after. She put on an act like she was bothered, but she wasn't i could feel it, and it was really awkward, like i didn't know if to call her mum or her name, so i never called her either. She didn't care about me finding her, she was more bothered about my other two sisters, i was another one of her unwanted children who came back.
Fast forward a couple of years, on new years eve, i sent her one long msg basically telling her how much i hated her, and then blocked her, and ive not spoken to her since, and i never will. So i knew her for two years.
The only reason why im sharing my story, is to say if you want to find your birth mother, you WILL find her eventually, don't let anybody stop you, your always going to want to find her, and until you do this urge will never go away.
Also don't expect miracles, hopefully for you things turn out good, and you can build a relationship with her, but just don't expect this to be an easy road.