Hi Jason,
I can understand your confusion and it’s a great point you make!
The fact is, that Blender starts counting at zero; the first ray hits a surface and that is bounce 0. A possible path with total Bounces set to 1 is:

So we have in order: Camera Ray > Bounce 0 > Diffuse Ray 0 > Bounce 1 > Diffuse Ray 1 > Light.
After a Bounce, there are many directions the Diffuse Ray can go, I just drew one possible path, that actually hits the light. The Rays that do not find a lightsource within the Bounce Limit, get ignored/ will not contribute to the lighting.