The International Olympic Committee said Bach wrote to Russian President Vladimir Putin to offer his condolences following the attacks on Sunday and Monday that killed more than 30 people in Volgograd.
A suicide bomber killed 14 people aboard an electric bus during Monday's morning rush hour, a day after a bomb blast killed at least 17 people at the city's main railway station.
"This is a despicable attack on innocent people and the entire Olympic Movement joins me in utterly condemning this cowardly act," Bach said in a statement Monday. "Our thoughts are with the loved ones of the victims."
Volgograd is located about 650 kilometres (400 miles) northeast of Sochi, which will host the Olympics from Feb. 7-23. Russia's first Winter Games are a matter of personal pride and prestige for Putin.
Russian authorities believe the two attacks were carried out by the same group. No one claimed responsibility for the bombings, which came several months after Chechen rebel leader Doku Umarov threatened new attacks against civilian targets in Russia, including the Olympics.
Bach said his letter to Putin expressed "our confidence in the Russian authorities to deliver safe and secure games in Sochi."
"I am certain that everything will be done to ensure the security of the athletes and all the participants of the Olympic Games," he said.
"Sadly terrorism is a global disease but it must never be allowed to triumph," Bach added. "The Olympic Games are about bringing people from all backgrounds and beliefs together to overcome our differences in a peaceful way."
Russian Olympic Committee chief Alexander Zhukov said there was no need to take any extra steps to secure Sochi in the wake of the Volgograd bombings because "everything necessary already has been done."
Still, the Volgograd bombings have brought home the security threat to Olympic athletes and administrators preparing to travel to Sochi.
Rene Fasel, president of the international ice hockey federation and head of the umbrella group of winter Olympic sports bodies, said security in Sochi will be similar to Salt Lake City when it hosted the 2002 Winter Games just months after the Sept. 11, 2001, terror attacks in the U.S.
"It will be very difficult for everybody. People will complain about security," Fasel said in an interview with The Associated Press. "I'm sure the Russians will do everything possible, but that means we will have an unbelievable (tight) security control."
Fasel said the Olympics should not bow to the terror threats.
"We have to be strong," he said. "We decided to go to Sochi and the only answer to these bombings and terrorist incidents is to go there."
John Coates, an IOC vice-president and head of the Australian Olympic Committee, said the Australian contingent would take precautions to keep athletes and their families as safe as possible, including restricting travel to flights only.
"None of our athletes will be travelling to or from Sochi by car, bus or train; none will be training or competing outside of Sochi in Russia; and, none will be holidaying elsewhere in Russia after the Games," Coates said in a statement. "Families of athletes and all other participants of the Olympic Games, including media and spectators, should note the steps we are taking for the safety and welfare of our athletes."
Norwegian cross-country skier Marit Bjoergen said Sunday she was frightened by the first attack in Volgograd.
"It's still difficult to say whether it has anything to do with the Sochi Olympics," she told Norwegian broadcaster NRK. "This came suddenly and I need to find out more about it. But one is slightly prepared for this kind of thing to happen and of course I'm a bit scared. I'm counting on that they will take good care of us and that we have good security during the games in Sochi."
Gerhard Heiberg, a Norwegian IOC member who organized the 1994 Winter Games in Lillehammer, said he was not surprised that bombings have occurred ahead of the Sochi Games but voiced confidence in the Russian security plans.
"I feel that everything that is humanly possible is being done," he told the AP. "When we come to Sochi, it will be impossible for the terrorists to do anything. The village will be sealed off from the outside world."
The British Olympic Association said it was monitoring the situation in Volgograd and was in regular contact with the Foreign Office, police, the IOC, other governing bodies and athletes.
"Our preparations for the Sochi 2014 Olympic Winter Games continue and we are confident the Russian officials will regularly assess the security measures that are in place to make certain the environment is as safe as possible," the BOA said.
AP Sports Writer John Pye in Brisbane, Australia and Associated Press writer Karl Ritter in Stockholm contributed to this report.