ammonia in tap water

My tap water has an ammonia level of about .25ppm (and a nitrate level
of 5ppm) from what I've been reading this is enough to be toxic to
fish. So my question is what should I do about it. My aquarium is in
the middle of a fishless cycle right now when I add 2ppm ammonia its
it's gone in 24hrs. So should I just use tap water and leave it to the
bacteria to take care of it. Or should I find another source of water.

My water comes from a private well and as far as I can tell there is
no chlorine. But the water is very hard with a high alkalinity and a
pH of 8.2. So what can I do to soften the water and maybe bring down
the pH.