There are lots of bamboo frame bikes around, it seems the idea is quite popular.
See here for example:
http://abstractdynamics.org/2003/07/growing_transit_the_bamboo_bic.php The issue seems to be jointing. Even if you use steel joints then at least that is cutting a lot of steel out of the bike, and making it lighter at the same time.
I think another issue would be durability, at least in some climates. Bamboo breaks down pretty quickly here when it is exposed to weather. The heat tends to make it crack and then it loses its strength, water gets in etc. I guess if you can just cut some new stuff and re-assemble it easily, its not a big deal. I don't know if you can use any natural products on bamboo to help protect it? I can't imagine it being very absorbent to waxes/oils.
Steel bikes can last just about forever if you look after them. There's about 2.5kg of steel in a bike frame, and at least 100-200 times as much in a small car (plus all the other stuff). So, making steel bikes for everyone would be easy if we did it now, but maybe not so easy if we keep depleting this other resources and it becomes harder to produce steel in the future.
Though the logistics of producing steel could get difficult if everyone is on bicycles, so perhaps it is a good question
