There are many bars in Chongqing, but most are underpopulated. Generally the local bottled beer is ¥10, and the variety includes several local beers and even Guinness expensive on occasions. If you go to one of the small restaurants to eat, you can buy bottles of local beer at ¥3 upwards.
As a warning, some bars have recently adopted a less pleasant method to send pretty girls to accompany and entertain you, and then ask for huge additional sums when you leave. Take care.