Oxford City Council is calling on the Government to step in and support them.
On Monday the Department for Transport provided additional support for train companies, temporarily suspending normal train franchise agreements and transferring all revenue and cost risk to the Government.
The Government said this would "ensure that trains necessary for key workers and essential travel continue to operate", adding that railways have already seen up to a 70% drop in passenger numbers as a result of the coronavirus outbreak.
Now, Oxford City Council is calling for the Government to provide support for bus companies so that doctors, nurses and other key workers can get to work.
It says Oxfordshire's providers have seen up to a 90% reduction in passenger numbers and are already operating at a loss.
The only Government support applicable to the bus companies is to furlough staff, with the Government then picking up 80% of the wage bill during the furlough. This would mean furloughing bus drivers, which would significantly impact services.
The Oxford Bus Company - which is further reducing its timetable on Monday - has said there is no level of service it can keep running that will cover its costs.
[COVID-19] These are very difficult times for all of us and so to support workers who need to continue traveling on our services, we've decided to postpone the fare changes previously scheduled for 5th April 2020. pic.twitter.com/1v6NbZCOFk— Oxford Bus Company (@OxfordBusCo) March 26, 2020
Councillor Susan Brown, Leader of Oxford City Council, said: "Oxford's bus companies provide a vital service to enable NHS doctors and nurses to get to work. Many of these key workers do not have cars.
"If the Government allows Oxford's bus companies to go under, many hundreds of key workers will no longer be able to get to work. This will have a profound impact on the NHS in the city.
"It is crucial that the Government provides urgent support for Oxford's bus companies - something similar to that already provided to rail companies - to ensure this does not happen."
Oxford City Council's warning that a bus company going under 'could have a significant impact on the county's NHS.'