Contracts to run 60 council-subsidised bus services in Bristol are being put out to tender.
Companies will be invited to bid to run night buses, park and rides and off-peak services for up to eight years.
A Bristol City Council spokesman said the authority hoped to increase competition to lower fares.
Fifty five per cent of bus services supported by the authority are currently run by First.
The company also controls 95% of non-subsidised services in the city.
Firms are being invited to bid by June 2011, and contracts would run from next September.
Liberal Democrat councillor Gary Hopkins said he wanted to encourage other large operators to consider coming to Bristol, and to see fares lowered.
The council held a meeting on Monday which 13 potential operators, including First, Stagecoach, Go Ahead Group and National Express, attended.
Mr Hopkins claimed a study had shown fares cost about £16 a week in Bristol, while in other comparable cities the figure was £12.
"Also, the one-off short term fares are quite high in some cases," he added.
Tony McNiff, managing director of First in Bristol, said: "From our perspective, our biggest competitor is the car. We are trying to encourage people out of the car and to use public transport."
He said in April, day fares had been reduced by 7% to £4, weekly fares by 10%, child weekend fares by 10% and family tickets by 5%.
The company was working with the council to improve congestion, he added.
"To be an operator in Bristol is not an extraordinarily profitable exercise," he said.
"We do make a profit but fares are indicative of base operating costs."
Funds also went into re-investment in services, he said.
The 60 contracts are currently supported by £5m of funding from the city council.
Mr McNiff said the company was anticipating more than £40m from councils in the Greater Bristol Bus Network area to improve "some of the issues which affect the travelling public".