"Miss B."
If "Miss B." is a Mount Holyoke faculty member, I'm confused as to who "Miss B." might be. Lydia Shattuck died one week before this letter was written, so it would seem reasonable that it was she, but the initial doesn't match. Elizabeth Blanchard, mentioned later in the letter, didn't die until two years after the letter was written.
Source
All information from One Hundred Year Biographical Directory of Mount Holyoke College 1837-1937, Bulletin Series 30, no. 5; published and compiled by the Alumnae Association of Mount Holyoke College, South Hadley, Massachusetts, and the 1889-1890 Mount Holyoke catalog.