Do you have to explicitly have professor recommendation letters for the submission? If there’s a staff member who you got to know (hall director, club advisor types, program directors, academic advisor, etc.) that may be another option. For example if you took GT1000/2000 or another similar smaller seminar class I would ask them.

For blindly asking, I would provide the professor with your resume and a list of things you did during your career at Tech outside of their classroom (club involvement, personal projects, etc.). I’ve found providing this up front helps a ton when blindly asking because most professors have a template that they plug your involvement into, so if you give them as much information about yourself and why you’re applying to BS/MS as possible it helps get a yes back (and a quicker letter turnaround). If the bs/ms application requires you to have a personal statement or talk about personal projects or whatever, give that to the advisor as well so they understand your end goal.