Surprising this is not available on the Web: I've burrowed around and cannot find it. It is probably Hollywood slang from the 1940s, when it was common to travel across the
US / Mexican border to get excellent dental work for a quarter of what you'd pay in California - remembering that anybody with aspirations to go before a movie camera must have a better-than-
perfect smile.
"Tijuana Dentist" is a euphemism for crossing the border to get a quick
abortion, if you happen to be an aspiring starlet who gets knocked up. In that era there was no
easy path to a legal pulling of the rabbit. So if you were expecting and did not expect to expect you would tell everyone you were going to Tijuana to get your
teeth fixed.