Replying to Boots/bindings for small and light girl

So I made a thread a month or so ago about skis for her, which she decided on (salomon lux 92), but it's time to decide on boots and bindings. Now here's the problem. She had a tiny foot. As in barely a 22. Anyone have suggestions on an adult women's boot that either runs true to size or even a little small? She got fitted but the shop didn't have anything that small on hand, and neither do most other shops in the area.

Secondly, any recommendations on a binding that goes down to either 3 or 3.5?

She's 5' and ~97lbs. Beginner level but athletic and quick to pick things up.