If you show up with a recorder and play a song, I think just about any group will be thrilled to have you.

The contact person is going to be called a chatelaine. These days, a lot of stuff is probably announced on a Facebook group, so it's also worth finding the one for your local branch and keeping an eye on it for meetings, classes, etc. (There's a whole ecosystem of special-interest SCA Facebook groups; I spend the most time on SCA Heraldry Chat.)

It sounds like your fencing teacher is also involved in the SCA, so if you express some interest, he might start inviting you to things?