Yep!

The free bus (the purple line of the Charm City Circulator [CCC]) that goes from Mt. Vernon to downtown picks up at the Washington Monument (Charles and Monument St.—as does the JHU shuttle, which you can just hop on if it comes first). Southbound CCC picks up at St. Paul and Madison or St. Paul and Centre. So you can easily hop on and save some steps either way if you want. The Circulator runs approximately every 15-20 minutes (supposedly), though it does not run late at night.