I'm inclined to say no don't do it. Bettas need to go to a surface often to breath and they are leapers which means you'd need to cover the top of the container. Lucky bambboo (not a real bamboo) normally needs a narrow vase type to get it to stand properly in water. That means less surface for the betta. It also could mean less room for the betta to swim making it a difficult environment for the fish. Lucky bamboos on their own will thrive for many years in water but they are not true bamboo. I have mine in vases getting filtered sunlight. No need for fertilizers but they can benefit from a weak dose of tropical fertilizers every now and then.

Lucky Bamboo is Dracaena sanderiana, a very easy to grow houseplant. Stripping off the lower leaves and growing it in water and calling it bamboo is a new trend for a plant that has been around a long time.

Yes, you can do it. In another tank that I had, there was one male beta with all the community fishies. In the back of the tank, where the filter is, there is the opening at the top to make room for the filter, you can insert one or several lucky bambos into the tank, but be sure its to the side of the filter water flow. As for having the lucky bambos in a vase with a beta, that is possible as well. Get a plastic cup (clear) and cut down to size. Cut a circle hole in the middle and insert several lucky bambos and adjust them. Place it on top of the vase and ta da! Yes, the beta will do great with it. The plastic cup holds the lucky bambos and prevent the beta from jumping out. However, be sure to have enough space for air at the top of the water. Do not listen to Ianna. I've done these before, as well with Ivy houseplants.