What is the shelf life of a garlic bulb, with the "skin" still on, left in the fridge?
Garlic will spoil faster in the fridge actually. I don't know how long it will last in the fridge, but I understand that it lasts longer if you leave it in a cool, dark, dry storage. I believe one reason is that your fridge is generally too humid. In my experience, garlic kept in the fridge is also more likely to develop mould (goes soft, and dark discolouration).

I keep mine in a ceramic thing in one of my cupboards. It lasts anywhere from a few weeks to a few months depending on the garlic (probably how long it sat before getting to my kitchen). If you store it like that, garlic that goes "bad" will usually start to sprout (green shoots, will come through the top.