Well, I made that up. I have no idea when they met or first appeared together.
But making things up seems to be the norm for stuff about celebrities (or often one's own ancestors). Take a look at this forum posting about Bud Abbott's 1900 census entry. Now take a look at the actual census. Notice how the poster made stuff up, particularly "Religion Jewish." Religion has never appeared on a U.S. census.
Others on the same forum commented on how the grandmother had a "Jewish name." This is in reference to "Rivka" which is what the earlier poster made up as the grandmother's name in the 1900 census. The census actually says "Reyka," a misspelling by the census taker of Ricka, a common nickname for Fredericka.
Here is Bud's mother Rachel, grandmother Fredericka, and grandfather Alexander Fisher (after whom Bud Abbott was named) in the 1860 census. This was long before Northern and Eastern European Jews started coming to the U.S.
So was Bud Abbott Jewish? It does not look like it based on the census info. But here is more grist for the rumor mill: In 1950 Bud and his wife renewed their wedding vows in a Jewish ceremony. Why they did this is not clear. Not do I understand why nobody in the ceremony is wearing a yarmulka.