The driver identified as Siddharth has been arrested, they said.
The incident occurred late on March 13 night after all passengers had alighted at Banashankari area. The woman from Punjab then asked him the way to Devegowda petrol bunk to which he said he would drop her at the spot.
After driving for some distance, he allegedly stopped the bus and tried to rape her, but when she raised an alarm, he got scared and drove the bus towards Chamarajpet, pushed her out of the bus after robbing her of her bag, police said.
Transport Minister Ramalinga Reddy today told reporters that three policemen attached to the police station had been suspended.
He said the driver has been suspended and the government would bear the full medical expenses of the woman to treat her injuries.