Cycle bugs is jargon for the beneficial bacteria that convert the ammonia to nitrites and then nitrates. You should do some more reading on cycling the tank if you are still confused.
http://www.kokosgoldfish.com/cycle.html From what I understand, the bacteria will grow on everything in your tank but the largest population on bacteria is living in the filter media. This means you should almost never change the filter pad, and if it is really falling apart and it needs changing, you should find a way to add the new filter media to the filter and leave it there for a while before you remove the old filter. This will allow bacteria to start growing on the new pad without killing the bacteria you already have. It is ok to (gently) rinse the filter media, but only in old tank water. The chlorine in tap water will kill the bacteria.
So the reason your tank is not cycling is because you get rid of them regularly.
Have you been testing for ammonia?