Building a bottle tree is something that I keep as one of those projects that I want to do but I keep pushing off. Are you thinking of building it for bottle storage, or also for drying? I want to build one for drying and I haven’t convinced myself what the best material would be.
If you decided on wood, teak is a very strong, durable option. Treated with either butcher block oil or solid coats of urethane, it would be waterproof enough to dry bottles without warping.