Pseudomonas aeruginosa is a pathogenic (causes disease in humans) bacterium. It is a common pathogen in hospitals, especially in things like whirlpool tubs, where it can cause problems for patients in the physical therapy department, especially patients who are being treated for decubius ulcers and burns. It is an ubiquitous (i.e. is found everywhere) organism, but in plumbing fixtures it seems to be found most often in the drains of tubs. For this reason most hospitals follow a protocol of cleaning their tubs and sterilizing the drains and traps with an antiseptic agent, and they monitor their plumbing fixtures by culturing swabs taken from the drains and tub walls.
Your WATER supply, however, ought to be bacteriologically pure. If you are able to culture Pseudomonas, E. coli, or other pathogens from your water supply, you have a problem. Contact your municipal water supplier. If you have a well, have that tested. It is possible that your water heater is contaminated. You can have that tested. If so, sterilize it (drain it, refill it, and turn up the heat for a while). You might consider installing a UV germicidal filter.