You may find that the water bottle drips so be prepared if more of her face and head get wet. Otherwise, it will probably solve the problem. She may be bracing herself to drink, so the water bottle might help that as well. Worth a try.
I’d brush or comb her now to see if she’s at the start of a shed. The can shed up to 4x/year, so if she is beginning to, it’s not unusual to see a bit of skin in thinly furred areas, especially if she washes herself regularly. Sometimes a bunny will overgroom a spot, or another bunny, in which case it can lead to a problem. If it’s wet because she is drooling out her mouth rather than getting wet from the dish, it could be a sign of a tooth problem. In that case, she needs to see a vet.
But I’d check out the hanging bottle and shedding possibilities first. Keep an eye out for redness or swelling which would indicate a medical reason as well. If so, see a vet.