Absolutely as Duck mentioned. The BEST bet you have is to buy a quality air stone. The quality ones stay at the bottom of the buckets AND produce better bubbled longer. If you wanted to go the cheap route, you could get something like this (I have these) hXXp://www.ebay.com/itm/Active-aqua-Air-Stone-Cylinder-Large-4-Pack-Free-priority-mail-shipping-/141119523962?pt=US_Hydroponics&hash=item20db610c7a
Just about the best stone you can get, will surely cost you a pretty penny, but will out bubble and out last any other stone on the market. Micro Pore Stone made for hydroponics basically. The single version is the cheapest, coming in at $15.00, but the best bang for the buck, in my opinion, are the Double's which come in at $29.00. Here's a link to a double, but with this new info you'd be able to search for the single, or even BIGGER than double.. all depending on your wallet and understanding of air stones. hXXp://www.plantlightinghydroponics.com/micropore-air-diffuser-double-p-1679.html
Next time I can afford it, I'm going to be investing into a BUNCH of the doubles! For now, I enjoy buying the Active Aqua air cylinders as I've tried many air stones until I was pointed their direction. I just get SO sick of my dang stone rolling around or floating around!
Hope this helps, but as PCDuck said, I wouldn't clue anything into your buckets as it makes it much harder to maintain and clean. In general, it seems like your only purpose to do that is to hold the stone down?
Take care and stay green