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 hopes new strategies will help it complete a U-turn that will get it out of the dead-end in which it finds itself.
Didi’s struggles in the bike-rental market led to a launch of its own brand, Qingju.
GGV Managing Partner Jixun Foo discusses the return to a more rational investment approach in China.
The rules went into effect on Wednesday on Didi’s bike-rental platforms Qingju and Bluegogo.