There are now shower facilities listed on the wiki logistics page. They are as follows:
Showers and meals are available free of charge to the homeless community at St. Francis House, a day shelter for the poor and homeless, located at 39 Boylston St. The shelter is open to everyone 18 years of age and older, serving meals from 7:30 to 9 a.m. and from 11:30 a.m. to 1 p.m. seven days a week. Showers are available Monday through Friday from 7:30 to 11 a.m.
Directions: To walk from Dewey Square to St. Francis House, walk down Atlantic Ave. past the South Station train and bus stations, turn right onto Essex Street, continue onto Boylston Street, and #39 will be on the right.
For more information, contact St. Francis House at 617-542-4211.