I am shortly going to be working on the muffler situation for my project. As I see it, the options are to purchase a muffler designed for a motorcycle (too loud), an ATV (a possibility), a small car (another possibility) or building one myself. I've been studying the design of commercial mufflers, but am still undecided.
Hey Alaskavan, that's neat, I hope you come up with something good. I seen that the bicycles at Spooky Tooth have a muffler coming from their motors. I don't know how much that quiets the sound. I also found this on bicycle-engines.com. I don't know if this would fit all 4 stroke engines http://www.bicycle-engines.com/standard-piece-muffler-p-143.html
I don't know anything about your Bridgestone motor. You will want to measure the port size and bolt spacing, and check with whoever you buy a pipe and muffler from to make sure it will fit. As far as the noise level for the mufflers sold for use with the 50cc 4-strokes (which may be about the right size for you), find a thread where somone has built their bike with a 4-stroke and ask them. They might also be able to tell you about pipe diameter and bolt spacing, too.
An idea I had for quieting things down. Every motocross rider out there is totally convinced that their stock muffler/silencer/expansion pipe is junk and the fancy aftermarket one will give them huge HP gains. Truth is it is usually a slight increase in high end HP at the expense of low end torque. Some guys buy one after market silencer then another when the next great thing comes along. Regardless, my point is there are 2 or 3 used mufflers for every bike out there. Even the stock ones are beautifully made ovalized alumiunm with billet tips, super high performance. My thought is to use the stock muffler that comes with my 49cc motorbike (cause I figure it probably creates the appropriate back pressure, could be totally wrong though) then attach a much bigger bore pipe and silencer for a much bigger engine, say a 250cc. The second silencer should be big enough to not restrict flow but still decrease sound to some degree. Of course I'll wonder if it would be faster without the original muffler and end up experimenting. You 2 stroke guys should look into adapting motocross expansion pipes because, again, there's 2 totally high performance pipes out there for every bike ever made. I want to start a thread on this idea when I actually start doing it. If you search ebay, there's tons, you could of course just use one from a 50cc.
Another thing to do is wrap the whole exhaust system with header tape. It's fiberglass strapping about 2" wide which contains heat and helps with noise too. As you are wrapping overlap by 50% so there is 2 layers. Hold it in place with bailing wire or stainless steele zip ties. Paint it black with silicone paint. You'd expect it looks ugly but it actually looks kind of cool, high performance race style. It's on ebay too or summit racing.