The AIIB, which will be capitalized at $100 billion, now has 57 members including most big European economies.
Mr Bernanke's remarks add to those of other senior U.S. figures who argue that Washington has mishandled its response to China's ambition to play a bigger role in the international economy.
Lawrence Summers, former U.S. Treasury secretary, wrote recently that U.S. cold-shouldering of the AIIB may be remembered as the moment it "lost its role as the underwriter of the global economic system".
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Mr Bernanke said those remarks were "a little strong" but agreed it was "unfortunate" that China had felt the need to go its own way. "It would be better to have a globally unified system and allow resources to go where they are needed," he said.
However, the former Fed chairman played down the practical implications of the AIIB, saying the bank was largely symbolic.
"There's now a huge amount of private capital flows going in and out of emerging markets, including money that goes into infrastructure projects," he said.
According to a former senior official at the Asian Development Bank, which is dominated by Japan and the U.S. ADB lending accounts for less than 2 percent of Asia's infrastructure needs.
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Mr Bernanke also said too much attention was being focused on the internationalization of the renminbi, which was as much a matter of "national prestige" as of practical economic value. In reality, he said, the Chinese currency's share of global reserves was "very tiny" and even its share of trade settlement was "modest".
China should continue gradual steps to open up its capital account, to deepen its bond markets and to allow a bigger role for the private sector, Mr Bernanke advised.
These were all preconditions to make the renminbi a reserve currency, he said, but they were more important as a means of improving capital allocation. The ultimate goal, he said, was to shift China's economic model from one dominated by heavy industry and investment to one in which the consumer and the service industry played a much bigger role.