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Bigelow said in her director's statement that she was "shocked" to learn men use "little more than a pair of pliers" to disarm a bomb that can kill within a radius of 300 metres.
She said: "When I learned that these men volunteer for this dangerous work, and often grow so fond of it that they can imagine doing nothing else, I knew what my next film was going to be about."
Other American films competing include The Wrestler, starring Mickey Rourke and The Burning Plain, a drama starring Kim Basinger and Charlize Theron.
Rachel Getting Married, starring Anne Hathaway, also competes, as does Vegas: Based on a True Story, centred on the life of a compulsive gambler.
Italy and Japan feature heavily, with Japanese animation Gake no Ue no Ponyo (Ponyo on the Cliff by the Sea) also in the competition.
A film which sees Natalie Portman make her directorial debut is also being screened during the festival.
Eve includes veteran actress Lauren Bacall in the cast.
The movie concerns a young woman named Kate, who visits her grandma Lola for dinner, and is surprised to find her grandma is on a date with a man named Joe.
Portman, who was on the jury at this year's Cannes Film Festival and is a Harvard University graduate, said in her director's statement: "I've always had a fascination with the older generation, particularly those who are not at ease with the ageing process."
Influential German film director Wim Wenders is the president of the Venezia 65 jury.
The festival is often viewed as a precursor to the Oscars.
Dame Helen Mirren won an Academy Award after winning a best actress prize at Venice for The Queen.
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