I see your misapplied ship icon and raise you a non-canon one.
The only person who calls Babs "Barb" is her father (which is a bit unsettling, since that's also what he called his ex-wife, but we can blame Miller for that and ignoring Miller is a well-honed skill of mine). If Ted somehow found this out he could have hours of fun with it.
(Ted should meet Jim. We know he approves of Dinah, we can be reasonably sure he approves of Dick, but Ted's still in the cold and you can't have a proper Babs OTP without Jim getting a chance to be happy about his baby girl being happy.)