First, I think it's great she is a water drinker. It's a great habit to encourage. At 13 months, I think that's proabbaly fine for her to drink water to hydrate in the hot weather. It's little babies they don't want to have water ("water poisoning").
Second, I would just keep offering milk. As with many things, she may just need to be exposed to develop a liking for it.
My daughter (16 months) has had occasional formula bottles since she was about 6 months. She transitioned to milk no problem. And I am still nursing once per day. I don't see a probalem with giving formula and seeign if she likes it. If she does, then start mixing with milk until you get to all milk. I have heard thar some people believe that you should nurse more than a year, and that with this in mind, formla fed babies should get formula longer too. You could pump too and mix it with milk, but I know tha tcan be a pain in the neck, especially when you aren't nursing that much to begin with.
I assume you are giving whole milk right? Little babies need the fats and protein. If you give less than whole milk, it may not be fatty enough in taste for her compared ot breast milk.
Buy a metal sippy so she can't see inside. But that will only get her past the first sip :) I believe babies should be off the bottle by 1 year, so I wouldn't encourage the bottle. Just give sippys. If anything, I would think she is mad to get milk in a bottle, because she expects breastmilk.
If you are still nursing 2-3 times per day, I would think that it would take a month or two to wean fully anyway? But regardless, you might want to give her a few weeks to adjust to cow's milk before cutting off her main source of milk.
Last thought, don't offer milk for a full week or two. then buy a brand new "milk cup" - let her shop with you. And then try again. Break the habit of her rejecting the cup.