The longer you let it acclimate to the new temperature the better. But if you are in a hurry, maybe 30-45 minutes minimum in the bag. Also, if you have some packets of silica gel that you get in shoe boxes, or when you buy new bags or things, you can throw those in too. It should help with the moisture.
For batteries, when shooting in the cold, keep a spare one close to your body. So if you are wearing a big jacket, put it in an inner pocket so your body heat keeps it warm. When batteries are cold, they tend to show as discharged when they still have power left. When the one you are shooting with gets to that point, switch the batteries. By the time the next battery is cold and registers as discharged, hopefully the first one, being next to your body, has warmed up enough again. Then just keep switching back and forth.