Free parking has been available at all county car parks since non-essential shops opened last Monday along with outdoor cafe and pub seating areas.
But bus users argue the initiative benefits motorists and disadvantages those who rely on – or choose – public transport, despite the council having declared a climate emergency two years ago.
Professor Les Lumsdon, of Bus Users Shropshire and Ludlow 21, said with businesses opening back up it was the perfect time to trial free buses.
In a letter to the council, he said Ludlow would be “an ideal town to trial it”.
“There’s little or no revenue at stake at the present, the approach fits with your climate change policy and is easy to administer with one bus company involved,” said Prof Lumsdon.
“There has been money devoted to promoting market towns which could be used to get behind this type of campaign.
“It would also be possible to monitor its effectiveness.
“We are most likely to be talking about far less than the revenue loss accruing to the free parking scheme.
“If that worked well in Ludlow then it could be rolled out onto the town services in the other market towns.
“Can I please ask you to reconsider this as a matter of urgency as it would send a clear signal that the council also recognises that those using sustainable modes shop and contribute to the local economy?”
Ludlow mayor Tim Gill said he would welcome a free bus trial in the town.
“I think this is an excellent idea and fully support it,” said Councillor Gill.
“About 70 per cent of passengers use a concessionary card anyway.
“But the proposal is also a good way to attract potential fare payers back to using the bus service which can only be a good thing, cutting down the use of cars coming into the town centre.”
Shropshire Council said it was “considering all options with regards to a possible public transport promotion”.
A council spokesman added: “It’s worth noting that English residents of state pensionable age or over, and those with an eligible disability, are able to apply for free or reduced travel by applying for the concessionary travel scheme administered by Shropshire Council.
“And for commercial bus services, any offers are in the gift of the bus operator, rather than the council.”