Bell was a silver medallist at the world championships earlier this year when he placed second in the pursuit.
He came out fast in the four-kilometre individual pursuit before fading slightly in the final laps to finish in four minutes 29.411 seconds. His time was fifth over the first 1,000 metres but 11th over the last 1,000.
That moved him up one spot to eighth overall going into the scratch race and time trial later in the day.
Norway's Lasse Norman Hansen, bronze medallist at the worlds, won the pursuit in 4:20.674.
World champion Glenn O'Shea of Australia led the 18-man field after four events, followed by Britain's Ed Clancy and Hansen.
The omnium covers six events over two days: flying lap, points race, elimination race, individual pursuit, scratch race and time trial. The winner in each one gets one point, the runner-up two points and so on, with the overall winner being the rider with the least total points.
In women's sprint qualifying, Calgary's Monique Sullivan was 12th with a time of 11.347 seconds.
The 23-year-old, a double gold medallist at the Pan American Cycling Championships, was sixth in the keirin last Friday. The keirin is an eight-lap race that sees riders jockey for position behind a motorized pace bike, which pulls away with 2.5 laps remaining to allow the final free-for-all sprint.
Britain's Victoria Pendleton had the fastest qualifying time with an Olympic record 10.724 seconds, erasing her own mark of 10.963 in Beijing. Pendleton won gold earlier here in the keirin.
On Saturday, Bell was seventh in the 250-metre flying lap, 13th in the points race and 10th in the elimination race to stand ninth overall after the first day of competition.
"Not a good start for me, obviously ... I'm not really sure why," Bell said after his first three races,
At the world championships in April, he was fifth in the flying lap, third in the points race and eighth in the elimination race.
He had 28 points after six events there. He has 30 points after four events here.
Bell, a 29-year-old from North Vancouver who grew up in Watson Lake, Yukon, some 400 kilometres east of Whitehorse, is a former World Cup champion in the omnium. He placed seventh in the points race at the 2008 Games in Beijing.