After a long pause Ulmer told about 80 children, aged between 6 and 12, she was "lucky".
"The media attention I got was really, really positive.
"It wasn't something I looked forward to, but it wasn't something I minded."
It was one of several tough questions put to Ulmer at the Queenstown Events Centre yesterday by children at Lakes Leisure's school holiday programme, leading her to declare the group "officially the brightest audience I've ever spoken to".
Ulmer's visit was to have coincided with the arrival of the ANZ Olympic Town Tour featuring a traditional London double-decker bus.
However, because of concerns about potential road conditions, the bus bypassed Queenstown.
The children were able to touch Ulmer's gold medal yesterday. Many of them were not even born when she won it at the 2004 Olympics in Athens.
When asked how she celebrated her win, Ulmer said she went for a run and then "I went to McDonald's and had a Big Mac".
"I still had another race three days later ... I couldn't really have a real party.
"This sounds really sad, but I went for a run.
"When you're a cyclist, you can't really do any other sports ... any other sport messes your body up for cycling.
"I hadn't run in about three years [so] after my race I went for a run around the Olympic Village."
She was also asked who her inspiration was - the answer: Dame Susan Devoy.
"She was amazing.
"The rest of the world thought she was a legend.
"Every time I saw her play ... or train ... she was always dripping sweat and just giving it absolutely everything she had.
"For me, she was my inspiration when I was 16 - there was this Kiwi woman beating everyone else in the world and beating them in a really cool way."
The children were surprised to find out Ulmer had not always been a winner.
When asked if she'd ever come "second or third", she told them if she had competed in 1000 races in her career "I probably lost about 980 of them".
"You lose most of the time, but you don't need to win very often to get the motivation to carry on.
"The Athens gold was really the first time we had set myself something to do in terms of going as fast as I could go, finding someone that could write a gym programme for me, finding someone that could write a training programme, finding someone that could build the bike, finding accommodation and working out where to train.
"It was the first time we'd put all the pieces of the puzzle together."
After speaking to the children yesterday Ulmer was joined by fellow former Olympian Hamish Carter and sports commentator John McBeth at an invitation-only function at the Queenstown Memorial Hall.
