Now, take my advice with a grain of salt b/c we still have not introduced milk (I am still nursing) and we never did bottles, BUT, if it were me, I'd just give up on milk for a week or two and offer other forms of dairy/calcium - yogurt, cheese, dark greens, etc are great calcium sources.
My daughter loves yogurt, and I make her yogurt smoothies once or twice a day - I mix yogurt with some fruit/veg puree and serve it in a take n toss straw cup, she loves them!
She also loves plain greek yogurt and it is good for practicing self-feeding with a spoon because it is so nice and thick and stays on the spoon.
Anyway, just some ideas, but I'd say, drop it with the milk for a few days, see how he does with yogurt instead if he likes it, and then try offering again next week or later on this week even. Just offer a lot of water after meals and you could do water at bed time - we do a sippy of water in the crib with her so she can take a swig if she wakes up thirsty and it works really well.