It's not quite accurate to say that "photons are waves in the electromagnetic field". The electromagnetic field is a classical approximation to the behavior of the full quantum photon field. Under some circumstances, the difference between the full behavior and the classical approximation can be striking. For example, any quantum field with a definite number of photons, no matter how large, has expectation values of zero for the classical electric and magnetic fields.
So, although this isn't exactly helpful, I'd say that photon waves are in the photon field, electron waves are in the electron (more accurately, electron-positron) field, etc.
What about a bullet? It can't propagate at the speed of light, since it has rest mass, but we can still address your question about its wave properties. For some composite objects one can approximately write a single wave for the whole thing in. For example, that procedure sort of works for C60 buckyballs. That approximation breaks down if internal vibrations etc. of the object are significant, in which case you need extra properties to describe the object. The behavior of an atomic nucleus can typically be described as a wave in a single field, since the nucleus is typically stuck in its lowest-energy internal state. The bullet will have many, many possible internal states and thus require a more complicated description. In principle, its wave could be written in terms of waves for the electrons, protons, neutrons, etc. of which it's composed. In practice, a classical description is far more practical.
(published on 05/20/2012)