distilled water is water that has been evaporated and condensated to remove impurities. bottled water may be boiled for sterilization, but boiling does not remove impurities. during distillation, water is is boiled to vapor, essentially sterilizing it. the vapor (steam) is collected and condensated in to another container.
my instincts tell me that bottled water would be more prone to being contaminated from the factory than than disitilled water, because the distillation process also sterilizes; whereas simply bottling water is not necessarily sterile.
either way, bugs will thrive on either just the same.