If you really want to strain, straining with cheesecloth leaves as much of the grease behind as possible while picking up the bacon particles. Paper towels over your jar/receptacle of choice will work, but will soak up a good amount of the grease.
I usually bake my bacon and pour off the grease to cook with. I think Mark has an article about how long bacon grease is safe for, but honestly, I keep it for months in the fridge sometimes. I always had more than enough when I was cooking bacon weekly. I don't have it as often now (too costly).