As I see it, most of the stars in the galactic bulge are Population I stars. However, as one moves farther from the galactic bulge, star metallicity decreases. In fact, halo stars are almost entirely Population II stars. Why is this?
It has to do with the formation of the Milky Way.
At the beginning, the Milky Way was much more spherical than it is now - perhaps closer to what an elliptical galaxy is like than a spiral galaxy. Population III stars would have formed first, then quickly died out. Next came Population II stars. They formed when the galaxy was still somewhat spherical, and so they tend to inhabit the galactic spheroid/halo.
Eventually, the rotation of the Milky Way flattened out much of the remaining gas and dust, and some of the stars. When younger stars formed, they formed in the flatter disk, nearer to the center. The disk itself became smaller that the spheroid/halo. Thus, the younger Population I stars are found in the galactic disk, and are closer in.
No more stars will form in globular clusters; they are relatively dust-free and contain old, Population II stars. The same is true for the galactic halo.
The galactic bulge itself contains several populations of stars. Some may have come from the halo and thick disk (thus being metal-poor) while others may have formed together more recently from the thin disk itself (thus being metal-rich).
The bulge population is old, older than 10 billion years. Its stars have a broad range of metallicities, but are more metal rich than population II, have an average close to solar metallicity and a significant fraction more metal rich than the Sun. The basic idea is that the bulge population is one that formed very quickly, with a high rate of gas infall and star formation. These properties lead to rapid ISM metal-enrichment (from supernovae and high mass AGB stars), a population with a broad range of, but high average, metallicity. An example paper on the subject would be Ferreras et al. (2003). http://m.mnras.oxfordjournals.org/content/345/4/1381
The halo population is older and formed at a relatively low rate (hence with a low ISM metal enrichment rate) before the Galaxy formed a disk. Hence the stars are still in a pseudo-spherical distribution and metal-poor.