I have a weed eater motor mounted on a mountain bike. The motor that I used was a Homelite 25cc. The shape and configuration of the motor makes it easier to mount to a bike. The one that I have sits over the motor and uses a jack shaft to power the bike. The tire scrubbers like this tend to ware the tires out fairly quickly. If you are gentle with the throttle, it isn't as bad. I bout a mounting kit off of ebay for about 100.00 and purchased a used motor from Lowes. After building it, I had to have a moped. There is a bike kit called a whizzer that might be a little faster (maybe a lot faster) and a little more dependable. If you look around the web, there are a lot of kits and a lot of differant ways to build one.
Good luck with you project.
BTW: I still use mine when I go on Bike rides. It is nice to be able to speed off after someone passes you on one of those fancy high dollar bikes. You do get great gas milage too. I carry a small container of gas (mixed) in the holder for a water bottle on the bike.