I'm sure the way most people ride their bikes, the bamboo would be plenty strong. That stuff is tremendously strong. Also notice that he filled the tubes up with expanding polyurethane foam, also light and very strong (it can even be used as a structural element in buildings). If you protect the ends of the bamboo, preventing it from splintering, then it is a great material. If it splinters, its all over.
I'm envisioning a bamboo chopper with big wooden handlebars..
peace,
sam