Right, this is just what I came up with in the short time I researched the info you gave me, so it could be wrong, but here we go.
The gits were a punk rock band fronted my Mia Zapata, active from 1986 - 1993. Orginally from Ohio, they moved to seattle and quickly established a following, which would make sense what with Seattle being into the whole grunge / punk rock scene back then.
So, I found you a band fronted by a woman,
from seattle
in the mid to late eighties
who, being a punk rock band could have used a breaking glass sample in a track.
All you have to do now is try to find the song.