This was a search question that led someone to my blog. Yes it is possible to be allergic to a bonsai tree. We can develop allergies and sensitivities to most anything we come in contact with over time. The other thought is that this person could not only be sensitive/allergic to the bonsai tree but if the plant is indoors they could be reacting to mold in the soil of the plant.
I don’t keep houseplants. I don’t want anything that will remain wet and set up an environment for mold to grow in. I have been recently thinking about growing plants in water to have greenery and to filter the air. I used to root philodendron plants in water and they would just grow like crazy in whatever jar I put them in. I did a little research and found that basically most plants can be grown in water. http://www.rodale.com/easy-houseplants
As soon as I can get some clippings I am going to start my own indoor plant garden. I promise to post pictures when I get my own going. Below are some plants that are grown in water.