Transport minister Graeme Dey said the money, which is being made available between October 4 and March 31 next year, would help operators “fill the gap” between the cost of running services and reduced revenues.
He said while passenger numbers had grown, following the success of the vaccination campaign and the easing of many coronavirus restrictions, this “additional support” was still required.
The money is on top of the funding operators get to run concessionary services, such as free bus travel for older Scots.
Announcing the additional funding, Mr Dey said: “Bus services played an essential role in keeping Scotland moving safely during the coronavirus pandemic – and have an equally important part to play as we gradually start to return to some sense of normality.
“Although passenger numbers have grown, additional support is still currently required.
“This funding of up to £42m means we can continue to fund operators between October 2021 and March 2022, to fill the gap between the additional costs of running services due to Covid-19 and reduced ticket income as demand recovers.”
The Confederation of Passenger Transport in Scotland welcomed the cash, with director Paul White saying it was “continued recognition of the vital role the bus network plays and the requirement to extend support while the impact of Covid continues to suppress passenger numbers”.
Meanwhile, Mr Dey urged people to plan journeys in advance, so they could avoid peak times if possible and to continue to adhere to the requirement to wear face coverings on public transport.
“I’d also encourage people to keep up good habits by continuing to walk, wheel or cycle where possible,” he added.
“The virus hasn’t gone away, so we need everyone to play their part in keeping our transport system safe.”
Train services have also taken a sustained hit across the pandemic.
It was revealed last month that 300 daily ScotRail services suspended because of the Covid crisis would not be restored under a planned major timetable change in May next year because of lower demand.