The all time quickest way to warm breastmilk without "cooking" it is to keep the milk in the milk storage bag and run it under warm water when it is time. It takes maybe 45 seconds to a minute and the milk is ready. If the water is too warm for your hand, it is too warm for your milk.
Then poor the milk into the clean bottle. I would take a clean bottle with me and a pouch or two of milk (sometimes partially frozen) to the store or where ever I was going. I'd be able to quickly warm the milk at a sink that had at least luke warm water and I'd be on my way.
Remember, milk doesn't have to be "warm" it can be room temp or cooler, but if it has been refrigerated then it has to be warmed enough for the fat to melt and immerse into the milk. You know it's not warm enough if the fat sticks to the inside of the bottle.