given the chlorine, etc. added to tap water, bacteria is probably not a concern however, if you are concerned about heavy metals (lead, etc.) know that simply boiling water does not remove them – worse is that the pure water is lost via the boiling (steam) thus after boiling you are left with a higher concentration of metals to water than you started with!
you can purchase a water filtration system that is fitted on your sink (replete with its own tap) or if you could find one of those jugs that has a filter fitted on it (brita is a brand that i bought at “HOLA” on hangkong road that is pretty good). problem here is that over time you will have to go out and buy mineral supplements as you will get no minerals via that filter.
for the record, when the guy came to install the water filtration system i made him test several of the commercial brands of water commonly sold (ie. nongfu spring, cestbon) and they were actually pretty clean.