I have had good luck purchasing the nut for an acoustic guitar and using that as the saddle, what you are calling the bridge. The saddle (bridge) is what transmits most of the string vibrations to the soundbox which in turns amplifies the sound. Your choice of material will influence the sound of your dulcimer. Yes, wood works. Softer woods will produce a softer sound with more overtones. The harder the wood, the crisper the sound. Some musicians will use very hard substances, including brass, to get a sharp twangy sound.
My personal favorite is to purchase a guitar nut made from bone. (Try ebay, less than$5, less than $1 if you can wait on shipping.) You will need to cut slots for the strings, in a pinch a common hacksaw will work. The clean sound produced will reward your efforts.