I don’t think that most bottled water is RO filtered. The brands that are produced from tap water are, from my understanding, mainly carbon filtered.
A carbon filter is cheap, easy to maintain, and easy to hook up temporarily for brewing use if you don’t go for a permanent installation (my own filtering system is of the temp variety…I hook it up on brew day and disconnect it as soon as the hot liquor tank is filled).
The only point I was really trying to make is that If your local water tastes good except for the presence of chlorine or chloramine, a carbon filter is a more economical way to go.
I (and many others) view bottled water as one of the great marketing scams of the 20the century (unless your municipal water is SO bad as to be unpalatable or if you have well water that’s a bit chunky).
As far as bacteria in bottled water goes, one shouldn’t assume that it is ‘purer’…there are published analysis indicating that many bottled waters actually have higher bacteria counts than average city water out of the tap! (of course, if you’re boiling it, it’s a moot point…just as it is with most tap water!)