After a year a year and a half went by, she asked him pointblank: "When are we gonna get married?"
He agreed it was a fine idea.
They were married in 1957 and this April, four children and eight grandchildren later, they will celebrate their 56th wedding anniversary. They moved to Pleasanton a few years ago to be near their family and have made friends at the Senior Center.
"He's very loving, very patient, very understanding, and let's me do what I want," Elsie said to explain the success of their marriage.
"I just keep quiet," Neil said. "When you start talking, that's when you get in trouble."
Also at the Senior Center was Irene Loos, who's been married for 68 years to her husband Harry. But she doesn't remember anyone proposing.
"I was 18 years old when we got married," she recalled. "It was right after Pearl Harbor and all the young couples were getting married so we got married."
"He was 20," she added. "We got married at our minister's home with our parents, in January 1943. We didn't have a lot of money."
This was back in Scotts Bluff, Neb., which they left 39 years ago to come to Pleasanton when their first grandchild was born.
Julie Parkinson, who works at the Senior Center and has been married for 31 years, met her husband Rick playing co-ed softball. His proposal came as a complete surprise.
"After Christmas midnight Mass we were sitting in his car in front of the house. I was 19 and I lived at home," she remembered. "He said, 'I have a question. Will you marry me?' I was totally unprepared and shocked.
"He even had the ring," she continued. "I was so excited."
Her husband sold that car, a Camaro, to pay for their honeymoon to Hawaii.
Meanwhile downtown at J'aime Bridal, it's all about brides, weddings and romance. Consultant Maureen Cindrick said she loves to hear stories about the proposals.
"Some are surprised, some are romantic. Sometimes the families are in on it," she said. "A bride yesterday was proposed to on the side of a mountain while they were snowboarding. They're getting married at Tahoe."
Bride Renee Swidler, 25, brought her groom Bobby Lee along with her to choose a dress last Friday.
"His opinion is the one that matters," she explained. She'd already been dress shopping with her mom and friends and said, "That experience was terrible."
Renee and Bobby have been a couple for two-and-a-half years, and she said they were prompted to become engaged and get married for a reason that is not particularly romantic: He has great health insurance.
"It helped us speed it up a little," Bobby acknowledged.
Now she is designing the ring, Renee said. "I know exactly what I want."
But it's up to Bobby to pick up the ring and figure out the best way to present it to her.
"I have a friend who got married in June. He got glow-in-the-dark stars and spelled out on the roof, 'Will you marry me?' and took her out to see it," Renee said.
The Internet is full of suggestions for ways to propose. There are hot air balloon proposals, ballgame proposals, treasure hunt proposals, poems, songs, trips and romantic dinners. One computer geek reprogrammed his girlfriend's favorite video game so that when she reached a certain score the screen went blank and a ring dropped down.
People have proposed via Twitter, Facebook, YouTube, and iPhone apps. Yes, there is an iPhone app for proposing as well as apps for every aspect of the wedding planning.
There is also a website called Proposal Gone Wrong so perhaps it's best to keep it simple. Of course it includes public proposals where the answer is "no."
Ashley Trujillo, 25, who's been married for five months, is also a consultant at J'aime Bridal.
"I used to cheerlead for the San Francisco 49ers," she said, and she became best friends with another cheerleader. At her friend's wedding, Ashley met and fell in love with the brother, Cion.
"Around Christmas I'd been saying, 'We need to get an ornament for our first Christmas together,'" she remembered.
One afternoon she came downstairs to find him standing by their tree, tears in his eyes. He reached for one of the ornaments and opened it to reveal an engagement ring.
"He said, 'I love you so much. I want to spend the rest of my life with you,'" she recalled.
Jerry Ridenour Leonardini also married the brother of her best friend, from back in the 1960s.
"He was the scary big brother a couple years older," she explained.
He was single again after 19 years of marriage and raising two boys while meanwhile she raised her daughter.
"In a comedy of errors I ended up seeing him in emergency when his mom had a stroke and I broke my leg," Jerry said. "We had a great time catching up while waiting for my leg to be cast."
They'd been a couple for four years and had even purchased a home together in Pleasanton by Valentine's Day 1998 when he presented her with a tiny box.
"I opened it and saw a wonderful diamond ring," she remembered, but he didn't say anything. "I asked him what it was for and he said, 'You know.'"
She's still waiting for him to pop the question, she noted with a laugh, although they went to Tahoe shortly after his non-verbal proposal and tied the knot.
Next time you see the bride walking down the aisle -- or maybe across the beach or meadow or along a forest path -- remember that it all started with a romantic moment when one of them popped the question. Or maybe they just decided that it was time.