Bamboo is one of my favorite materials for flute making. Yet, Bamboo is very sensitive to humidity, maybe more than any hardwoods traditionally used for flutes.
I treated my first bamboo flutes about 20 years ago with Parafin Oil. I was very disappointed: after a while, all my flutes are splitted and cracked. Turns out the Parafin Oil is evaporating from the material.
I then started looking for different oils to protect my flutes and started to use oils which are hardening and stay in the wood on the long run.
Linseed oil is one of the best for bamboo flutes but takes a little while to dry. You may also use Biopin Oil. It's a mix of different oils and waxes and it dries very quiqly.
When you receive your bamboo flute, it has already been treated with oil. You can play on it immediately after receiving the flute.
My advise is that give a litle bit of oil inside of your bamboo flute ones a month and also put a bit of oil on the ambusher hole as well.
Here's what I recommend to protect your bamboo flutes and keep them a long time: Linseed oil, Almond oil, Tung oil, Yoyoba oil.