If you take a gander at the bottle feeding board we are discussing the very issue that most of our little ones will take water or juice from a sippy NO problem, but put milk in there and it a big NO NO!!
Try offering finger foods when he could be hungry, I personally do it;
e0730 bottle and breakfast
A
s 1030 -1100
Snack on waking
E lunch @ 12noon
A
S1430 - 1530
1600 - dinner
Snack at approx 6pm when DH and I eat dinner.
E1830 milk
bath, milk, bed......