It's all dependent on what essential oils you'll be burning, you need to do specific searches for each essential oil you are going to use, and check to see if it is known to have any bad interactions or effects on Reptiles in-general, not just Bearded Dragons. Each essential oil is totally different than the next, some are perfectly fine, some are lethal.
Either way, keep the diffuser away from your dragon's tank so that it's no where near him, so that he won't be breathing any of it in directly, as they are very susceptible to Upper Respiratory Infections and irritations. I'm a parrot owner so I can't use ANY types of oil diffusers, scented candles, etc. as birds can be killed almost instantly from breathing-in such things, so I haven't done a whole lot of research on individual essential oils and reptiles, I just don't use them. However, you're correct about Tea Tree Oil, it's not recommended for use around birds or reptiles. As for any other ones, the best advice is to individually search each different oil you use, and if you see any negative indications then do not use it in the same room as your dragon, it's just not worth the risk.
