After I swap out my bandsaw blade for another, I'm left with a large hoop of sharp serrated metal.
How can I store this safely.
You can "collapse" them into much smaller hoops (see http://www.woodmagazine.com/woodworking-tips/techniques/skills/folding-bandsaw-blades-simple-as-one-two-three/). It brings it down to about a third of the size and can be stored in a drawer.
From the page:
Hold the blade in front of you with one hand, keeping the teeth pointing away from you. Wear a glove if you've got one handy. Put your foot inside the loop and step on the blade, securing it firmly to the floor. Simultaneously rotate and lower your hand as you hold the top of the blade. By the time your hand makes three-quarters to one full revolution, the blade will have popped into three coils.
They can be hung in an out of the way corner.
Ideally on a piece of wood with a curved channel the blade rests in so the it doesn't kink.
Most of the time they can be twisted onto one another and looped if you're careful. I gently twist a wire twist tie to hold them in shape. Then you can hang them up with less issues.