The council put Chester City Transport, which trades as Chesterbus, on the market in the summer because it could not afford to invest in the 78-strong fleet.
However, as Arriva North West & Wales plans to run buses that will mimic Chesterbus' routes and timetables, the council fears Chesterbus could be driven out of business before it is sold.
Chester has launched proceedings under the Competition Act 1998, asking for a court order to stop Arriva.
Leader Paul Roberts (Lib Dem) said: 'We simply cannot allow such bullying tactics to go unchallenged.'
However, Arriva North West & Wales managing director, Bob Hind said: 'Their allegations against us are unfounded and inaccurate.
'We have made it very clear that our intentions were not to disrupt the market, but to create a seamless transfer.'