The cash pledge, which was announced by the First Minister at a briefing on coronavirus in Edinburgh, is intended to help support companies during the outbreak.
Under the current agreement, Transport Scotland reimburses bus firms for travel under the concessionary scheme for over-60s and disabled people.
Nicola Sturgeon announced this year's funding will not be based on the true amount of travel but projections made at the beginning of the year.
Drop in travel
According to Transport Scotland, bus operators will be able to access the £260 million available to support the concessionary scheme and bus service operator grant payments.
The difference between projections and the amount that will actually be paid to bus operators over the next four months is expected be between £46 million and £92 million, Transport Scotland has said.
According to Ms Sturgeon, concessionary travel has dropped by more than 70% since the beginning of the outbreak.
Transport Secretary Michael Matheson said numbers have dropped 81% in the last two weeks and are expected fall further after recent Government advice.
‘Very challenging time’
The First Minister said: "I will also confirm today to support these companies at this time the Scottish Government will pay them for the concessionary travel they were forecast to provide, rather than the concessionary travel that they do actually provide.
"That will deliver support worth tens of millions of pounds to bus companies at a very challenging time."
Mr Matheson said: "We are doing everything we can to support our bus industry in this unprecedented time.
"This action will enable critical services to continue to run, helping our key workers get to their work and to carry out their essential roles across the country.
"I also recognise that our bus industry will be vital to our economic recovery - and we must take steps to protect that recovery now.
"People are changing their travel patterns to help reduce the spread of coronavirus and we've seen a real dip in public transport use across Scotland."
He added: "Over the next few months we will effectively make up the difference in concessionary travel and Bus Service Operator Grant payments.
"We will allow operators to access the £260 million that we spend every year on supporting bus services, irrespective of the decline in passengers.
"This will help protect the industry, support our key workers and ultimately assist the nationwide response to the Covid-19 outbreak."
Commenting on the emergency support for the Scottish bus industry through coronavirus, Anthony Smith, chief executive of the independent watchdog Transport Focus, said: “Around half of bus passengers tell us that the bus is the only real means of transport available to them, so it is right that the Scottish Government has recognised the exceptional circumstances posed by coronavirus.
“Bus operators must survive to keep services running in these challenging times and get back up and running again as soon as this is over.”