What neurons' projections comprise the olfactory nerve (Cranial Nerve 1)?
Olfactory receptor neurons (ORNs) in the olfactory epithelium in the nasal cavity project to the olfactory bulb; this projection is Cranial Nerve 1 and it's more of a collection of fibers rather than a highly organized nerve.

Your surprise or confusion is probably based on this:


  My understanding is that the projections that emanate from the olfactory bulb and terminate in the brain constitute the olfactory nerve


...which is false: the olfactory nerve is the step prior to the olfactory bulb. The olfactory bulb is part of the brain.

I'll add that I have seen poor diagrams of the brain that point to the olfactory bulb and label is as cranial nerve 1, which is false or at least misleading.