Local Government Association (LGA) analysis found the free bus pass scheme was underfunded by about £652m in 2017-18.
It said councils were having to fill the gap between government funding and the cost of the scheme, with free bus passes for off-peak travel being a legal entitlement for those over 65, or those with a disability.
However, the constraints have meant local authorities have been spending less on discretionary services such as free peak travel, post-school transport and supported rural services.
Almost half of all bus routes in England receive partial or complete subsidies from local councils.
The services are at risk as councils struggle to maintain the current levels of support, the LGA warned.
It called on ministers to bring back full funding of the costs of the concessionary travel scheme.
"An estimated funding gap of £652m a year for concessionary travel is unsustainable for councils already struggling to protect other subsidised bus travel in rural areas, or helping young people with their travel costs," said LGA transport spokesman Martin Tett.
"Properly funding the national free bus pass scheme is essential if the government wants councils to be able to maintain our essential bus services, reduce congestion and protect vital routes.
"If this is not addressed in the spending review it could lead to older people having a free bus pass but no bus to travel on."
Department for Transport figures showed local bus journeys in England fell by 85 million - or 1.9% - in the year ending March 2018.
The councils say more than 3,000 supported bus services since 2010-11 have been either withdrawn, reduced or altered.
"It is for councils to decide which bus operations to support in their areas, but we help to subsidise costs through around £250m worth of investment every year," a Department for Transport spokeswoman said.
"£42m of this is devolved to local authorities and a further £1bn from government funds the free bus pass scheme, benefiting older and disabled people across the country."