We recently did MXP to Turin on Flibco bus. You would have to check if they go to Aosta. Also check Flexbus.
For our Flibco bus MXP to Turin Porta Neuvo:
1) At MXP, be aware that for the olympics earlier this year, they moved many of the buses from just outside the terminals at MXP to the other side of the train station/hotel. So to get to Flibco, Flexbus, and several others, go down in the terminal, following signs to train, bus, hotel. You end up walking thru a tunnel that goes under the road in front of the terminal. Then an escalator up and you are basically in the train station. Go straight thru it a short distance and come out on other side. Turn right for entrance to hotel and left for all the bus stalls.
2) This was our first really long/ "out of town after international flight" bus ride and I was a little concerned that it might be loud and cringy. In fact the bus was very clean and very quiet.
Hope it help.