There are many different opinions on how many species of bamboo that there are. Some experts say there are approximately 1000 species of bamboo, while others say there are more than 1600 species on the planet growing naturally.
It would be hard to make any specific recommendation on bamboo species as there are so many and I am not sure of your local. I have no real opinion on what is available in North America other than the kind that grows at my parents place, in Ontario, is weak and not good for much.
You see things like bamboo poles for fencing. You could split those with a knife fairly easily to get the lengthwise strips that you would need for this. Buying an entire fence seems excessive though. However for where and what it is used for it should be more than sufficient for what your are doing.
You might have better luck if this is a one off project by using something simpler like a bamboo placemat. You should be able to find one of these easy.
You can take that apart and get (almost?) the lengths you need and there should be enough strength in there to get the job done. Also would not have to finish or cut it yourself.