Bamboo bikes are not a good idea, as bamboo deteriorates much faster than steel, aluminum or carbon fiber. It is a novelty, not a good idea for a bike you want to last for many years.
If you decide to make a bamboo fork, I suggest using at least 70 mm bamboo from near the base of the bamboo. Near the base, bamboo has a thick wall, and a small hollow center. Higher up, it has a thin wall, and a large hollow center. Similarly if you made one out of pine, you would want at least 2 by 3 inches. Anything thinner would not be strong enough.
If you want the bamboo look, drill out the middle of bamboo, and slide it over steel or aluminum forks.