1/4" is still a chicken strip. Just a very small one.
Actually, that might be about the most you can expect from the Busa. Not sure since I've never ridden one, but it's completely possible that you'd be scraping hard parts (pegs) before you got all the way to the edge of the tire. Also, it depends on the tires you're running. Some permit greater lean angles, and thus are more difficult to run all the way to the edge, than others.