Plant Coloration Stabilizer
You're looking for a mordant or fixative, such as potassium alum, $\ce{KAl(SO4)2·12H2O}$.

Though I do not know how well this will work on wood, mordants are often used on textiles. Check for cotton and linen mordants in particular, since they are cellulosic material, like wood (though wood also has lignin, which may inhibit uptake of the stain).

You might ask your teacher if she thought you are too young to dye.