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.