In P mode, the Auto ISO setting is greyed out.
That would be in the menu "ISO sensitivity settings" > "ISO sensitivity", right? Correct, the "Auto" value can only be selected in some scene modes. In P mode, you have to select a numeric default. See the table in the manual, page 54.
But, on another forum I found the answer:
When ISO Sensitivity Auto control is enabled, the camera will endeavour to use the ISO you set, but will increase the ISO automatically (up to your defined max) if it's not achieving the shutter speed set in the menu. If you actually take a shot then check the settings used on the LCD, you may well see that the ISO will be a different value, and shown in red, to indicate that the camera took over and adjusted it automatically.
So, not a completely Auto ISO, but I guess close.
Should I leave the ISO on 100, and let the camera bump it up if needed?
Yes, that would be a good option to start with.