While I have not found anything on the bonsai tree in particular, there are many household plants that are very toxic to your birds. The link below has a good site listing many, many different kinds of toxic plants. It's good that you are wary of the possible affect that plants can have on your bird because many bird owners don't even think there could be a potential hazard!

Some plants are so high in toxins that they can even kill your bird! (example is the Oleander) Now the bird COULD be a hazard to the tree... God knows how birds love to chew things, so you'll still need to watch them.
