Another way of Finding Biological Mother?

Depends on where in the world you are will depend on how easy or hard it will be to apply for and get your adoption file...where I live it is easy once you are 'of age' you can apply to social services and will get it along with help/support/advice from social services to investigate, in other countries you have to pay and file in court and try to persuade the judge to unseal and release a copy to you, so that can be hard and expensive with no guarantee you will get what you want. So that is the first thing I would do, investigate what right you have to get a copy of your adoption file....you have a letter from "the agency" so contact them as they have your file.
Write down on a piece of paper what you do have and work on that, do not concentrate on what you don't have..so surname, school attended, so you also have the city/county where she lived and was also liking born in...if you do not have an age minus 15-25 years from your date of birth...then the local library ( also online searches) does the school have year books, do they have a website, is there an old classmates page on social media, so you search those for the surname, the old electoral rolls and phone directories...there maybe websites where you can search those, the library ( or local records office) will have them, each time you find some potential information you write down where/what document/website you found it and what it is...it maybe several people with that surname thy are potential siblings/parents if not her, basically you are like a police investigator you find all and anything you can based on what you already have/know and start to build up more information, some of which might not be relevant to your finding her, other information could be

Facebook will let you search for people based on their name and high school. If she is on facebook and she told FB her high school, you might find her.

Most high school graduating classes have someone on the reunion committee who knows names and current addresses of SOME of their classmates. You'd have to have a rough idea of her age.

Ancestry.com, which you can access for free from some public libraries, has yearbooks from some high schools digitized. You might find her there. They also have some city directories digitized. If the name is uncommon, you might find her parents.

If you Google "Adoption registry" plus the state you were born in, you will find several. Some charge, some don't. Basically you post the date and time you were born, the place, and anything else that will help. If she sees it and feels like it, she replies. Be careful there; someone from Benin or Nigeria may pretend to be her and ask you for money. Someone from the shady side of town may pretend to be her and ask you to meet up.

Maybe type in her last name with parentheses and her high school name with parentheses on google and lets say there are 12 entries you can narrow it with ages of the person and stuff like that.

If you are adult,hire a private detective to help you

You obviously have no idea how to research. You might start by doing DNA, which would cut down the possibilities greatly.
You know her surname, and what high school she went to. Many Schools have alumni sites, I would start there while I was waiting for the tests results. YOU need to know if your adoption was a closed adoption or not and if you were adopted at birth.
If a closed adoption you will probably not be able to get information on it. If you were adopted at birth you only have one birth record and that is the one with your present name. Would love to help you further, but Yahoo doesn't allow me to provide my name and address.