Exactly how I handle them, when they get dull, I pull out a new replacement and the dull one goes into the bin. I'm sure I could learn to sharpen them, but life's too short to spend time doing that. 
Sharpening a bit by hand on a grinder the right way does take time to learn, and takes a certain "touch" of skill. The Drill Doctor makes it easy, almost fool proof, and takes about a minute to do if you're slow. Chuck the bit, insert chuck in Doctor, slowly spin while gently pushing, done. You cant walk from your car to the drill bit isle, or fill out an online order form that fast. The #750 does 3/32" to 3/4" in multiple angles and adding a spilt to each is optional each time. For ten years, Ive only had to buy the little bits.
I do keep assorted dull bits for the brittle plastics too. Gives softening thru melting a little before it cuts. Ive also melted holes in plastic, running bits high speed in reverse.
