Are you meaning in a pot of water? Or putting the bamboo in the tank?
Ive kept a male betta in a 3 gallon vase (with water of course) with a bamboo plant (I know this is not the most acceptable environment for a betta, but will do if cared for correctly). He lived for 2 yrs before dying.
Just make sure to do a Partial water change everyday (I done this by replacing a half a cup of water from the vase. Also, Make sure to dechlorinate
). This will prevent ammonia and nitrite build-up within the vase, keeping it safe for the betta.
As long as you keep the water clean (By doing the water changes) the water shouldn't be murky. Also, If you are worried that he doesn't have enough oxygen, dont, the Bamboo acts like a source of oxygen.
If you are meaning putting a Bamboo plant in the bettas tank, It will be fine as long as the leafs on the bamboo are out of the water. If not, they could die and decay in your aquarium leaving ammonia.