Transport Minister Stewart Stevenson said the replacement crossing was vital to the economy.
"Given the real uncertainty of the future viability of the current Forth Road Bridge, Scotland simply cannot afford any delay to the Forth replacement crossing," he said.
"That is why we are taking the earliest possible action to prevent serious disruption to cross-Forth traffic arising from maintenance and repair works on the Forth Road Bridge."
An alternative £1bn offer from the Westminster government to help pay for the project has remained on the table, but Scottish ministers have dismissed it as a red herring.
An artist's impression of how the new Forth crossing should look
They argue the bridge is a "once-in-a-generation" project which should be paid for over a longer period of time, rather than within a few years.
Labour finance spokesman Andy Kerr said the Scottish government still needed to show the proposals stood up to scrutiny.
"The SNP are failing the credibility test over the new Forth bridge by producing a bill that fails to say how the new crossing will be paid for," he said.
Scottish Liberal Democrat transport spokeswoman Alison McInnes said a better funding solution was needed, adding: "The SNP needs to swallow its pride and work with the UK government to sort this out."
The condition of the existing bridge has been deteriorating
Tory Lothians MSP Gavin Brown, said: "We cannot take the risk that the existing bridge is closed to traffic within the next 10 years - to cut off the east of Scotland and Fife from Edinburgh and the south is simply unthinkable."
Green MSP Patrick Harvie said: "Never before has Holyrood been presented with such an unaffordable Bill, a ten-figure sum to replace a bridge that doesn't need to be replaced.
"Even assuming the price wouldn't spiral out of control during construction, it's already the most expensive bridge of its type ever proposed."
Environmental group Friends of the Earth Scotland said the new crossing was unnecessary, as official figures showed the existing bridge would cost a maximum of £122m to be repaired, while the £2bn cost of the new one would be better spent on public transport and other green projects.
Edinburgh City Council transport convener, Gordon Mackenzie, also raised concern.
He said: "I welcome the publication of the bill - but call for a firm commitment to provide the other public transport measures, such as park and ride, which would be required for it to work effectively.
"Spending over £2bn to have the same traffic queues, or worse, is not a sensible position for the Scottish Parliament to adopt."
The bill is expected to win parliamentary approval by the end of next year, with construction due to get under way in 2011.
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