I've been living in Shanghai for 4.5 years. Before, I would only drink bottled water... even local people in Shanghai drinks bottled water. And a year ago, I have installed a water softener, and a water filter at home, then, I start to drink boiled tap water, which I think is more healthy.
This past February, I spent about 10 days in Shanghai while on vacation from the US. I drank boiled tap water since that's what my in-laws provided. I had no problems.
You can drink it.
That's what common people and their kids drink here.
My suggestion for a bottled water is Nongfu Shanquan that is mineral and coming from a natural source in Zhejiang.