You can almost certainly get a copy directly (and anonymously) from the New York Attorney General's office website. Go to the AG's office's Charities Bureau online. (https://www.charitiesnys.com/home.html) Enter the name of the 501(c)(3) in the "Search Charities Registry" box or use the "Advanced Search" and search by the school's EIN or other identifying numbers. Once you find your school, there will be a list of available documents, which should include the bylaws or other organizing documents.
You can file a request with the IRS to receive a copy of a 501(c)(3)'s application for exemption, which might have included their bylaws as part of the request. But the form (Form 4506-B) requires you to identify yourself and the reason you are requesting the information).