The Roger Williams Family Association's 1987 "Descendants of Roger Williams" [supplement published 2003], in its "Waterman Line" compiled by Dorothy Higson White, assigns Bethia Waterman the maiden surname of Waite... but it does not specify, from among several sources listed, which (if any) of them are the basis of this claim. (Jacobus & Waterman's "Waterman Family", Vol. III, is listed, but it is clearly _not_ the source, as it agrees with Anderson's GMB in leaving Bethia's maiden surname blank.)
It is true that "Waite" appears fairly often in succeeding generations as a _given_ name, which is a nice piece of _oblique_ or circumstantial evidence, but it is hardly conclusive on its own. Bethia and Richard are among my direct ancestors and, as in other such cases, I'd very much like to know my 8th great grandmother's birth name. But I'm not sure even the RWFA truly knows what it is.