If your child is younger than 12 months, I would refrain from giving cow's milk altogether, see What Happens If a Newborn Drinks Cow Milk? and Cow's milk: When and how to introduce it. Problems which can occur are nutritional deficiencies (most commonly iron deficiency), gastrointestinal irritation or allergic reactions. In general, babies' digestive tracts and kidneys are not yet ready
Living in Germany, UHT-milk is quite common, which can be stored up to nine months, if not opened. Then it should be consumed within a couple of days - one week works fine for us at home including our three-year-old.
For a day out, I recommend using a vacuum flask together with drinking cups; as of 1 year our son as well as all children in our nursery school were well able to use that instead of a bottle.
We generally dispose all "unfinished" drinks at the end of the day, I would do likewise with an unfinished bottle (i.e. keep it one day maximum).