When it came to love, the third time was certainly the charm for .

The legendary entertainer, who  on Jan. 17, had married Army Air Forces pilot Dick Barker in 1945—and divorced him that year, too, after he tried to bring the Beverly Hills High School graduate home to roost on his Ohio chicken farm. "A nightmare," she called that experience.

Then, in 1947, she tied the knot with Lane Allen, an actor turned talent agent. Their union lasted barely two years, White beating her retreat when he wanted her to stop working so much, though they remained friends.

Her career in radio and TV subsequently took off in the 1950s, highlights including starring in and producing the sitcom 

, for which she won a Los Angeles Area Emmy for Most Outstanding Female Personality, and hosting her own eponymous talk show. While she had boyfriends, the legally unattached life seemed to suit her.

So by the time a 39-year-old White met host Allen Ludden when she started appearing on the CBS show, one of many game shows that welcomed her as a favorite celebrity guest through the years, she may have felt a spark right away, but she was in no rush to connect for the long haul.

Not least because she was seeing another man and Ludden, 44, was newly widowed, having lost his first wife (and mother of his three children) to cancer just weeks after 

premiered on Oct. 2, 1961.

He was "never too busy to say a warm good-bye after the last show finished," White, who made her first appearance in the show's third week on the air, .

And then their agents—"you know how they are," White quipped during a —booked them to star together in a 1962 summer stock production of , a comedy about a theater critic whose wife writes a play and he's unsure of whether he should give her an honest opinion, at the Cape Playhouse on Cape Cod.

Ludden later said he fell in love with White on opening night.

"We were up there for three weeks and pretty soon he didn't say hello, he'd say, 'Will you marry me?'' White recalled to the TV Academy. "It was a joke! I'd laugh it off, he'd laugh it off. And then pretty soon I came back home. I was going very steadily with someone!"

And her boyfriend, Phil Cochran, was a little perturbed by a lengthy kiss White and Ludden shared in the play at one point. "It went on and on," she remembered of the night Cochran, who served as a fighter pilot during World War II, came to see the show, recalling a loud "coming from the audience.

"Everybody thought it was hysterically funny, except Phil," she said.

"Phil didn't think it was funny. He said, 'I don't like that guy.'"

White returned to Los Angeles (and, for a little while longer, Cochran), while Ludden, who was based in New York, got busy pining away—and proposing for real. "That went on for a year," White explained. "And finally it wasn't a joke anymore and I'd get mad. I said, ', no way.'"

Undeterred by her initial refusals, he bought a ring—"a beautiful gold wedding ring with diamonds all around"—and for three months he wore "that damned ring on a chain around his neck so I couldn't miss it," White remembered in her 1987 memoir . "It got full of soap and suntan oil, but he vowed he would only take it off for one reason.

"

But "in love as I was, nonetheless," she recalled, "marrying and moving east was still not in the equation."

Still, he'd use up all his time off from to visit her in California and repeatedly ask for her hand.

Ludden finally got to slip that ring on his beloved's finger after Easter in 1963, when his gift of flower-shaped earrings studded with diamonds, rubies and sapphires pinned into the ears of a fluffy stuffed bunny proved too much to refuse.

"So when he called that night," she told the TV Academy, "I said, 'OK, .' And afterwards he said I'm the only woman in the world who said yes to marrying him not for the earrings, but for the stuffed bunny.

"

Reflecting on why she did fall for him in the end, White in 2010, "What got us together was his enthusiasm. He was interested in everything. There wasn't anything that he didn't want to know more about and hear about. That's fun to live with." And, she also said, "What you saw was what you got. He was one of the nicest, dearest people."

"They just connected on all levels," Jeff Witjas, White's longtime friend and agent, exclusively told E! News. "From what I remember from talking to Betty, Allen was very charming and he loved Betty dearly, and he was a very passionate man.

"He pursued Betty for awhile, until she said yes to getting married.

So you've got to give him a lot of credit, he knew what he wanted—and Betty knew what she wanted. She just wanted to be super careful in the beginning, and it was probably one of the best moves she ever made in her life."