As the time approached, I became very anxious about the expedition but supposed a few would go with me. Finally I could not find a single member of the company who were sure to go. I went forward with my preparations, however, and to the extent I could, I purchased an outfit which consisted of a wagon and some provisions, a rifle, and ammunition.
The rifle was “an old flint-lock rifle, but a good one.” He had been told by experienced hunters that cap or percussion locks were unreliable if they got wet, but if he lost his flint he could always pick up another on the plains.
How Stuff Works has a good description of how a flintlock fires, with this diagram.
It is interesting that presumably, until this time, John Bidwell did not have a gun. Or if he did, he traded it for this old but reliable flint-lock.