Is it safe to store applejuice in an opened glass bottle outside of the fridge?
Most of the apple juice sold in the US at least is Pasteurized. So unopened, you should have no problem storing at room temp. Once you open the bottle, microorganism's can get in. With a sugary liquid like Apple juice, wild yeasts will find a happy home, and ferment up a bubbly alcoholic apple beverage for you. This can take a week or two to happen, and the result is usually tasty rather than deadly. Sometimes you'll end up with vinegar rather than an alcoholic ferment.
There's some small chance of picking up a nasty microbe in your apple juice over a three day period, but it was never enough to stop people from drinking unrefrigerated cider in the days before Pasteurization or refrigeration.