You do NOT want to use bleach...it may probably forever become part of the bowl, as far as fumes/taste/& toxicity, & anyway, bleach will NOT remove the deposits.
Soak full of white vinegar until the hard water deposits soften & can be scrubbed off. Vinegar is also a mild disinfectant, but I'd use another (F10 or chlorhexidine)
after the vinegar & rinse, just to be safe. You probably could use CLR, with a very thorough soap scrub & rinsing after (instead of vinegar) but I wouldn't take the chance.
What's this bowl made of? Hard plastic? or ceramic? (if it's not plastic, you could bake it too, I suppose, to kill germs)
BTW, you can find all sorts of inexpensive bowls (not necessarily designed for pets but for people) in thrift stores that cost very little too. Nothing "soaks into" glass,
so it's safe once cleaned thoroughly.
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