Yes, definitely only one t.... Betsy .
Spelling rule: Betty needs two ts for pronunciation reasons: like jetty or Netto.
Betsy doesn't because the "s" provides the second consonant.
I can't be doing with people who spell their kids' names in ways that go against the rules of pronunciation (don't get me started on the ones who called their daughter Lilley[sic] and insisted it was pronounced Ly-lee)