See 1814. The earlier meaning is not certain.

1

1766.  The utility of Tubs, Cags, and Dumb-Bettys.Boston Evening Post, Jan. 13.

2

1814.  Jefferson’s Dumb Betty, which without the attendance of a servant serves up his chocolate and hot muffins for breakfast.—Mass. Spy, May 14: from the Salem Gazette.

3