The petition was discussed by Ludlow Town Council’s representational committee after gathering around 100 signatures.
It said the town was being blighted by excessive noise caused by groups of bikers riding repeatedly around the one-way loop, and raised concerns over health and safety relating to emissions and alleged speeding.
Councillors were divided over whether the regular visits from bikers were welcomed or not, but said they had no powers to prevent them coming in either way.
Councillor Robin Pote said: “This has been an ongoing thing for a very long time, and I have to say that in my opinion its nuisance value is greatly exaggerated.
"There is little to no evidence that the motorbikes are speeding around the town. I do accept they come in to be seen because they’re very proud of their bikes.
“It’s a public highway and, as far as I understand it, we have no authority over controlling whether these bikes come in or not.
“I just feel it’s a small number of people who unfortunately, from where they live, may feel this is an affront on their private space.
“But I simply feel that as long as there’s no real breaking the law – and that hasn’t been proven yet – that there’s nothing we can do about it.”
Councillor Rod Naysmith backed Councillor Pote’s views, saying: “Personally I like to look at the motorbikes when they’re all parked up.”
Councillor Naysmith said if there was any law-breaking the police should be called to deal with it at the time.
Councillor Viv Parry said some of the bikes did make “tremendous amounts of noise”, but added that to bar bikers from the town would cause traders to miss out on potential income.
She said: “If we tell people that they can’t come I think we are being a little bit petty, but maybe the noise could be brought down slightly.”
Councillor Philip Adams said the council should issue a statement asking bikers not to rev so much in the town centre.
Town clerk Gina Wilding said the town council could ask Shropshire Council to carry out noise monitoring, to help to establish the scale of the problem.
Councillor Parry said the town also had problems with “boy racers”, and monitoring would also measure the levels of noise from these vehicles. Councillor Colin Sheward, chairing the committee, proposed going down that route, which was unanimously agreed.