In a letter, Dan said the South Yorkshire Passenger Transport Executive (SYPTE) did its best to mitigate cuts by operators but added a ‘complete rethink’ was needed.
The mayor also said he found late-running services and cancellations ‘frustrating and infuriating’.
South Yorkshire’s bus services are currently subject to a county-wide review and a report detailing what should happen next will be published in the spring.
Dan said: “While SYPTE does its best to manage and mitigate service cuts by operators, its architecture and approach are no longer fit for purpose.
“For far too long we’ve had more of the executive than the passenger - a complete rethink is required. Arms-length arrangements have also cemented a gap between funding and accountability, and we have lost sight of where this accountability sits.
“The travelling public has in recent years been subject to steadily deteriorating services as the frequency, reliability, connectivity and the general quality of our buses spirals downwards.
“I am working to arrest this decline, though there are no easy solutions. I have inherited annualised reductions in funding for buses, ultimately attributable to government cuts, resulting in a situation of ‘managed decline’ where passenger patronage has fallen steadily.
“But we also need a fresh, imaginative approach to how we run local services, including exploring the creation of not-for-profit and co-operative bus companies and expanding public ownership and local, democratic accountability throughout our public transport system.”