So, if I understand this correctly, O-Sensei taught jo to simulate spear and bayonet techniques, and then awarded a bo system to a single student. Where did this system come from?
Well, I would only say what my teachers have said and what I have personally experienced, which is that O-Sensei taught the Bo form and the Jo form ( again, I am referencing the Shingu lineage) as very flexible methods of weapons training which allowed the practitioner the most multi-dimensional weapons corollary to technique.
My teachers and I also express what we were left with through O-Sensei's Bo, calligraphy, and verbal teachings, which is this: it was inspired of Nature. Literally, I have been taught, the system O-Sensei transmitted at the time came from Nature. Our job as deshi has been to open our minds and to learn what this means.
If the question you are asking is 'what was the weapons lineage?', I will again quote Aikido Journal: " Hikitsuchi engaged in intensive training with Ueshiba, centered on the sword. As I described elsewhere, Ueshiba’s aiki principles are contained in three forms he adapted from Yagyu Shinkage-ryu. Hikitsuchi trained extensively in jukenjutsu as a young man, and was very skilled in both iaido and kendo. "
These are the teachings I have received. I sincerely hope they can be of some help in your understanding and practice.