Mini bikes are loud because they have no mufflers and are powered, in effect, by lawn mower engines. In order to quiet a mini bike down, you need a muffler for the engine. You can select from a variety of mufflers that will tone your bike down to a dull roar or even make it nearly as quiet as an electric bike.
Items you will need
Clamps
Select one or more potential mufflers from your local hardware store. Check the return policy before you buy to be sure that you can bring the ones back that don't work for you. As a rule, the larger a muffler is, the more sound-deadening material inside. So for starters, let's say you have a 5 horsepower motor. Go to your local hardware store or small engine repair shop and get a muffler rated for a 20 horsepower engine.
Clamp the muffler onto the exhaust pipe of your mini bike's engine. You don't need to clamp it excessively since you're just trying it out. Most mufflers fit smoothly over the exhaust pipes and only need a few clamps to hold them in place. Some actually come with mounting equipment so you can screw them on.
Fire up the engine and decide if the muffler is sound-deadening enough for you. If it is, then move on. If not, try a larger muffler.
Fix the muffler securely to the mini bike. Use additional clamps and any mounting equipment that came with the muffler.
Ride your mini bike around. If you've added a huge muffler, you may have some trouble balancing. Make sure that the muffler suits your riding style and doesn't interfere with steering.