Why does the Milky Way Galaxy's nuclear bulge contain many red giants and supergiants as opposed to dwarfs and other stars?
We do not know that to be true.
The fact is, astronomers have only recently been able to map our galaxy's center. That most red giants are at the center is not in dispute. But astronomers at the Keck Observatory have great difficulty in observing our galaxy's center for two reasons, 1) it is extremely bright and individual objects (stars) are tough to nail down because they are moving at great speeds, and 2) there is a great deal of cosmic dirt between us and the galaxy's center further clouding our observations.
There could be millions of dwarfs at the center but in that they are extremely small, we could not detect them with today's technology. Dwarf stars are tough enough to detect away from the brightness of the center because of their small size and relative low luminosity.