As someone who doesn't speak horticulturalist, might I suggest a list of species that belong in the Moraceae and/or Rosaceae families and are common in bonsai?
For me, some possibilities appear to be,
-apples
-crabapples
-pears
-ume
-wild rose varieties
-flowering quince (boke, and chojubai)
-spirea varieties
-pyracantha/firethorn
-photinia
-Chinese quince
-hawthorn
-cotoneaster
All of these belong to the Rosacea family, but this is what I've managed to find combing through my books.
For Moraceae, the only thing I can think of is a mulberry, which I've already been looking for for some time.
^Feel free to add to this. These are all common in Japan, but of course all of us in different places have access to different things.