Bath and North East Somerset Council is considering a public space protection order for Abbey Church Yard, Kingston Parade and Abbey Green.
The council said the order would "stop unwanted disturbance" in these areas.
There is currently no formal policy on busking in the city as performers follow a voluntary code of practice.
In September an evensong service at Bath Abbey was stopped when loud music from buskers outside made it "impossible to continue", the rector, Rev Edward Mason told the BBC.
Rev Mason said the use of amplifiers by buskers has "massively increased" in recent years.
According to the council, the number of complaints about amplified busking in the city centre has risen from 30 in 2012 to more than 110 last year.
The authority said, buskers were "an important part of the vibrancy of Bath" and the protection orders would ensure "activities don't have a detrimental effect on the quality of life of those in the locality".
A public consultation has begun into the proposals. A public space protection order can be put in place under the anti-social behaviour, crime and policing act 2014.
Buskers in Bath may be banned from using amplifiers in three central locations following more than 100 complaints to the council.