I am about to graduate college in May 2019 with a BFA in Performance and Production. My emphasis is for Stage Managing but I am strongly considering teaching now.
You might want to think about getting some professional experience before grad school for some
if you plan on teaching.
My S is an MFA student at YSD and was admitted straight out of undergrad. All YSD theatre disciplines, to include stage management, are top-notch.
Check out Emerson @ https://www.emerson.edu/academics/theatre-education-ma
Try College of Charleston - I think they have BA not sure about MA. Also Emerson.