In America, we usually say baby bottle for feeding an infant. Milk generally comes in cartons or jugs these days.

In the past, we always bought general-purpose milk in glass bottles, so when we hear the term 'milk bottle', that's what we think of. So. you're right - the term 'milk bottle' doesn't suggest a baby's bottle. In the context of feeding a baby, we generally just say 'bottle', because it's clear what we mean. But if, for example, you are in a department store that has different kinds of bottles and you want to specify what kind you want, you might say 'baby's bottle' or 'feeding bottle'. I wouldn't say 'nursing', though - talking about 'nursing' a baby when you mean feeding is quite old-fashioned now.