For a bunch of whole leaves, it's all about avoiding excess moisture. Wrap the bunch of kale in a layer of paper towels, and store in a supermarket plastic bag or a zip-top plastic bag in the refrigerator crisper drawer. The kale should be in great shape for a week.
Do kale need to be refrigerated?
Kale should be stored in the refrigerator, and kept in a plastic tub or bag. Since kale needs to breathe, it's best if the bag or tub does not seal completely, but allows for some air flow. ... Be sure to keep the kale away from the back of the fridge, where temperatures are often much lower, and the kale could freeze.
Can you store kale on the counter?
Kale tends to get more and more bitter the longer it is left at room temperature, so keep it cool, sucka'! I tightly wrap my kale in a paper towel and then place it in an air-tight bag. Now, since kale bunches tend to be rather large, that is not always possible. Just get the bag as air-tight as you can.