The seeds need to be mature. That is, the seed capsules are brown and have opened slightly so that you can see the little black seed inside.
In that case I just pick them, let them dry on a paper towel for a day or so, then rub the flower spikes around on a small gauge strainer. Mostly only the seeds go through.
Can't you wash your leaves? What kind of bugs did you have? One reason I love to grow herbs is that nothing (insects, critters, etc) bothers them, but apparently that is not everyone's experience (Susan W recently posted about all the bugs eating hers).