Centre for Cities has put bus franchising as one of its three recommended priorities for whoever replaces Dan Jarvis as the region's mayor after next month's election.
It said: "Unreliable bus services are a major problem across South Yorkshire, where the current privatised system has led to a lack of services, fragmented routes and expensive journeys.
"Franchising would allow the new mayor to coordinate the routes, schedules and fares of the bus network, making bus travel more accessible and attractive for people living and working in South Yorkshire."
The idea is already under consideration in South Yorkshire, following Andy Burnham winning a legal battle to press ahead with the process in Greater Manchester.
Currently, bus services outside of Greater London are deregulated, provided by commercial operators who decide their own routes and timetables and also retain control over their revenue and profits.
Under the proposed Andy Burnham scheme, Transport for Greater Manchester would set routes, timetables and fares for a number of different franchises, which bus operators would then bid competitively for.
Centre for Cities has said improving education and skills for young people and driving growth in Sheffield city centre should be the other two key priorities for the region's next mayor.
Centre for Cities Chief Executive Andrew Carter said: “As South Yorkshire emerges from the pandemic and grapples with a growing cost of living crisis, the new mayor will face huge challenges to repair the damage and get the region on the path to success.
“Whoever is elected on May 5 will need to work closely with local businesses, councils and the Government to level up South Yorkshire by boosting skills, overhauling public transport, and driving growth in its urban areas.
“Failing to prioritise these policies will slow recovery and potentially hold South Yorkshire back from reaching its full potential as a hub of high-skilled, well-paid jobs.”
The report highlighted that South Yorkshire is behind other areas of the country when it comes to educational performance.
It said: "Currently, every local authority across the South Yorkshire area performs below the national average in school achievement. For example, 47 per cent of students in England achieved at least a grade 5 in both their English and maths GCSEs in 2019, but only 42 per cent of students in Barnsley, 39 per cent of students in Sheffield, 34 per cent of students in Rotherham, and 33 per cent of students in Doncaster did so.
"While the new mayor of South Yorkshire will not have any direct powers over schools, they should use their high profile position to champion the improvement of primary and secondary education attainment.
"This can be done by bringing together school leaders from across South Yorkshire to discuss common difficulties and establish best practices for improving education across the region and championing the work of education charities to inspire young people to learn and ensure they develop vital skills for successful careers."
Centre for Cities said that a lack of office space combined with poor transport links means Sheffield is underperforming compared to other cities across the UK.
It said: "The total number of jobs in Sheffield's city centre fell by two per cent between 1998 and 2015, while they grew by at least 25 per cent in other northern city centres, including Manchester, Leeds and Liverpool.
"A lack of quality public transport links is also damaging Sheffield, where just 35 per cent of residents can reach the city centre within 30 minutes by train, tram or bus.
"Encouraging the construction of more office space in Sheffield’s city centre, while boosting demand for them by building housing near key transport routes, should be a key part of the new mayor’s strategy to drive growth and increase prosperity in South Yorkshire."
The report comes as Centre for Cities today launches its City Minutes: South Yorkshire Election Special podcast series, featuring interviews with mayoral candidates on their plans for the region.
Interviews with Simon Biltcliffe (Yorkshire Party), Oliver Coppard (Labour), Joe Otten (Liberal Democrats) and Bex Whyman (Green Party) will be published across the week. The two other candidates - Clive Watkinson (Conservatives) and David Bettney (Social Democratic Party) were invited to appear but have not recorded episodes.
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