I wouldn't use it for a couple reasons...it can be injested and certainly will cause problems. Also, it absorbs moisture and thus, bacteria can grow and harm the dragon. Though Aspen is great for most small mammmals, I really don't think it would be good for a bearded dragon. I have heard snakes do well on aspen (ie corn snakes) but even then it is recommended the snakes not be fed on it due to risk of injecting some of the aspen. Since dragons like to 'taste' their environment, injesting of some of the wood is possible.
This is just my personal opinion based on comments regarding other forms of wood (ie repti-bark, wood pellets etc). I have not used it nor would I want to risk my dragon's health, especially considering what I use now is much safer and cheaper. (ie plastic tablecloth).