Defending a push to move the census from once every five years to once every 10, the bureau's chief executive David Kalisch said the census did less than was generally thought.
There is a sense in the community that a lot of information is derived from the census, which isn't true
While the census was useful for setting electoral boundaries, infrastructure planning and business decisions, it was "an increasingly modest input".
"We believe there is a different way of configuring our statistical approach that makes use of a census and also makes better use of more regular population surveys," he said.
The bureau has asked the government to relieve it of the legislated requirement to run a census every five years. The next one is due in 2016.
The United States and the United Kingdom each run censuses only every 10 years.
Asked whether there would be a census in 2016 as scheduled, Mr Kalisch said he could not "announce what the government might decide".
Asked whether he wanted to be freed of that obligation to conduct the 2016 census, Mr Kalisch said he shouldn't disclose what he had put to the government.
The bureau wanted to reallocate funding away from the census towards upgrading its technology in order to continue to produce high quality statistics.
"You talk about the people having trust and faith in the bureau," Labor senator Sam Dastyari told him. "How do you build trust and faith when the one interaction that all Australian people have with the bureau is the one thing you've put on the table to get chopped?"
The hearing took place as the trade union United Voice launched an online petition at SaveOurCensus.com.au...
National secretary David O'Byrne said cancelling the census would marginalise his members and vulnerable Australians.
Among the workers United Voice represents are cleaners, childcare workers, restaurant and hotel employees and ambulance officers.
"Our members in childcare rely on the census to prepare for the 308,065 births each year," he said. "Our aged care members need accurate data to provide services for the 3,012,300 older Australians. As the union representing 21,626 baristas and hospitality workers, we need this data to ensure workforce training is adequate."
A bureau spokesman responded that the births figure didn't come from the census, and the each of the other examples could have come from somewhere else.
"This is a good example of what we are talking about. People ascribe a whole lot of stuff to the census that is actually delivered through other vehicles."
"The union is not right about births. Certainly the number of older people and number of hospitality workers does come from the census, but it is also produced by the bureau on a more regular basis through other means."
In The Age and Sydney Morning Herald
. Play with the census. It's fun and interactive
. Sunday Explainer. What is the census and can we afford to do without it?
. Blowing out our brains. Our census faces the axe (video)