Mostly depends on the rabbit's preference on bowl vs. bottle. I find most times, given a choice, buns will drink more easily out of a bowl.
Water intake varies wildly also depending on the bunny and on how much they get from veggies. A lot of people find their buns don't drink a lot of water at all. They hardly ever catch their buns drinking. Mine slurp a little a couple times a day. But, I have 1 rabbit who will dive into every bowl of water I give her. She slurps up 3 whole cups of water if left to her own devices, and two vets she's seen have both told me that it's perfectly normal (after having ruled out illness). I don't give her that much because she literally can't control her bladder with that much liquid, but it just gives you an idea of the spectrum. Most don't drink a whole lot, but it's important to make sure that you check water level daily to make sure that the bottle is still working, there's water in the bowl and that they haven't tipped it over and spilled it all out.