Beijing and Shanghai have given no indication of whether the bans will be lifted.
Other bike-rental companies are considering raising prices, as warmer weather brings a likely rebound in trip numbers.
Chinese bike-rental firms, Mobike and Hello Transtech, expressed their willingness to enter the bidding.
The law comes as concern mounts about the financial stability of a number of mobility firms in the rental economy sector.
Didi’s struggles in the bike-rental market led to a launch of its own brand, Qingju.
The rules went into effect on Wednesday on Didi’s bike-rental platforms Qingju and Bluegogo.