That looks rather less like an airship and more like how draped in a fishing net is "neither clothed or naked" for traveling over the water.
And is bamboo strong enough?
Bamboo is strong enough, especially if you use laminate. For many purposes of airship construction, so is high-quality wood. Lots of early airships used wood rather than aluminium, and they flew just fine.
The real problem is not doing it with premodern technology, though it is hard to see a society placed to figure out the details (see my hypothetical volcanic bamboo jungle whalers). Propulsion will be an issue, but theoretically, even a muscle-powered airship can work as long as the wind is not against it. The problem is that you still need a large and well-developed network of trade routes, technical expertise and labour organisation to build that thing, and I can't see a bronze-age civilisation mustering that.