I still get anxious over this with my Umbrella Cockatoo and I have had her for a long time (I see her drink one-two times weekly). To appease my own anxiety, I give lots of watery fruit/veg (shoot for more veg than fruit because of sugar content)...
I don't give much citrus (small "cutie" wedge 1-2 times each week and my bird is big) and I avoid veggies high in oxalic acid (for instance, spinach may be given, but not daily and 1-2 leaves at a time for mine)...
If you can get your bird to try fruit/veg (safe types) then at least you know they are consuming fluids, but I do think some birds are sneaky drinkers.
Keep changing the water etc.
FYI---If a vet or someone ever tells you to mix meds with water, do not do it for this very reason.
Also, my "Too" drinks a lot when I give her a glass pie plate filled with water (which she splashes in)..obviously not the most sanitary, but bathing is another opportunity.
If you do one of those closed bottles, please know that not all birds know how to use them, so if your bird is drinking, you might confuse him/her with a different bottle. You could present both and see if you see a difference, but I wouldn't assume that your bird understands.
Finally, was the bird drinking tap water from the same area before or something else?
Birds can get weird about the flavors of different waters..
My bird loves the crappy water at my parents' house but she isn't too fond of purified water (which I give her daily). She didn't even visit my parents for a long time, so this preference is very odd...and I know it isn't the best water for her (lake -type water...rural area).