The shutdown means the 70,000 daily journeys across the bridge will have to be re-routed, which would take an hour longer via the Kincardine Bridge, even with no extra traffic.
Tailbacks of around seven miles built up yesterday morning on the eastern approach to the Kincardine Bridge, with other long queues elsewhere.
Stagecoach, the main bus operator using the bridge, said it had diverted services via that bridge, but warned passengers of delays.
A spokeswoman said it would also run extra buses between Fife and Edinburgh “wherever possible” to help ease traffic congestion.
A dedicated bus corridor on diversionary routes, along with park and ride sites, is being considered by ministers, who are also looking at possible cross-Forth ferries.
However, a far wider impact is expected on the Scottish rail network next week after ScotRail said it would switch more carriages on to trains over the Forth Bridge.
The operator admitted this would increase overcrowding on other lines, which are already struggling to cope because of the shortage of diesel trains.
ScotRail re-deployed carriages from the Edinburgh-Glasgow via Shotts and Glasgow-Falkirk Grahamston lines yesterday and will announce where it is taking them from next week over the weekend.
Transport minister Derek Mackay said the action was justified because the bridge closure was a matter of “national significance”. He said: “There has to be a degree of understanding in other areas.”
ScotRail is also trying to get more trains from elsewhere in Britain, and press its trains being refurbished back into service.
A spokesman said: “We’re already using every train we have at our disposal, so we must consider other ways to add capacity to trains between Fife and the Lothians. The most effective action we can take is to reduce services on a handful of routes where other public transport options are available.
“This will enable us to add more carriages on existing services over the Forth from Monday – and perhaps extra trains when possible.
“As the peak hours will be the busiest, the best thing that people could do is to try and stagger their journeys.
“Travelling outwith the peak periods will have a significant impact on the number of people that will be able to travel over the duration of the closure of the Forth Road Bridge.”
Robert Samson, a passenger manager at watchdog Transport Focus, said: “The closure of the bridge will put additional strain on the rail network and trade-offs will have to be made in deploying scarce rolling stock.
“The priority at this difficult time must be to meet demand as best as possible.
“ScotRail must work hard to deliver a robust train plan that gives passengers sufficient information to make informed travel choices.”
However, Mick Cash, general secretary of the Rail, Maritime and Transport union, said: “The sudden and enforced closure of the Forth Bridge has seriously exposed the chronic lack of spare rolling stock and capacity on ScotRail.”
Dr Steve Cassidy, a director of transport consultants ESP Group, said there was now an opportunity for commuters to re-think their travel.