In English, "I want some milk" doesn't really refer to a specific amount. It doesn't actually mean that you want a small amount of milk, it just means you want milk. It usually refers to a generic/average/normal amount, so in the case of milk, it'd be one glass. Or if you said "I want some cake" that'd probably mean one piece of cake. Is it the same in Dutch?
No, all three expressions originate as referring to a piece that is bit off from a larger piece. In Dutch and in German they have been generalised to the point that we can apply them to liquids such as milk as well. In English this is not the case. "A bit of milk" is still nonsense in English because you can't bite milk.