Hello oloPocram and derpelikan,
I am doing "Italy" on the BD soon, and this much I have found out.
Rome is unreliable for new first and new bus.
At the moment it is designated old, but the odd new is flying there.
HOWEVER.......!!!!!!
The 346 which I love flies out of Milan all the time.
For me it was no problem, as I can catch the Pendilino up and down, and across.
I have been advised, *G can use the Swiss/Lufthansa lounge, but they may have other facilities for F. enjoy your travels.