How do you insulate the floor of a bump out?

It's sort of like an exterior wall lying on its side, with the bottom exposed to the weather (Hardie Soffit), but you can't get in there to spray foam on the soffit once installed.
It's not exactly like the floor over a crawlspace because it has the bottom of the "joists" sealed.

Do you stuff some fiberglass batting up there and then put the Hardie soffit panel up with a piece of 2" rigid foam glued to it?

Or do you stick the foam up to the subfloor, crack seal around it and fill the cavity with a batt before the soffit panel goes on?

How does permeance work with the floor covering, subfloor and the soffit panel?

Where is the exterior vapor barrier?

I don't see why you couldn't foam the whole thing if you wanted to. Don't forget; it's got sides or walls, too. Whatever you sheath the sides with could be put on after foaming, or cut access holes to inject the foam. It could be foamed from underneath, though- they foam roof decks all the time. The soffit is just there for aesthetics and to protect the insulation. If you're really worried about thermal transfer through the floor joists, you could apply sheet foam, then the soffit over it- just like a wall.

The problem is that we don't want to call the spray foamer out to set up for just a few small places.

Of course, the thought of just going ahead with the soffiting and then drilling a few holes to fill it up with foam later is pretty attractive......