I have a 3 year old and 21 month old. Both of them get thirsty through the night and so they keep a sippy with water in their beds. Usually 1 filled cup is sufficient for the night, but occasionally they will call to get a refill. If she regularly needs more than 1 cup, I'd fill a couple and leave them there. Others mentioned changing sippy cups to a harder top variety. We have a variety of different kinds. Both of mine will chew on the "Nubby" ones and usually cause them to no longer be leak proof in a short time so they do not get them in bed (actually we've just got one left that really needs tossed.) There tons of different ones. Maybe let her help you pick out a new kind as a special treat. You should be prepared with no more than 4 that you pre-approve as leak-proof and safe for her to choose from. Once she picks, you don't want to have to take it saying it's not safe or leaks. If she's really opposed to the harder tops, I think some have a semi-soft top - maybe it's Gerber. We have lots of Playtex cups and mine have always liked those. Mine think the bigger Playtex cup that is designed like a coffee mug (still leak proof) makes them very big. It's more like drinking from a cup. We also have an insulated set with Elmo which they love.
I transitioned both of my kids to sippies at 6 months when they started eating food in a chair. When they ate at the table, they got a sippy with water to practice learning how to use it. It kept them amused while we ate. They only ever got water in the sippy (well VERY rarely I'd add a bit of juice to the water, but it was very diluted.) They both nursed and I am at home with them so they rarely used bottles espcially after 6 months since at that point I could hold them over with food and water until I could nurse them. After they weaned, they did start drinking soy milk (neither likes milk) in the sippies but only at the table or when watching a show on tv (MAYBE 30 min/day).