When she is flying at least in the Broadway production. She has a bit more then a minuet and a half to be down there for the bows. There is a tad bit more action after she flys but not a whole lot. But, surely enough to buy her a bit of time.
Also, one thing that you have to realize about the backstage area of the New Amsterdam is this. That it can get pretty cramped back there. It is not only a matter of her getting down there in time but also everyone moving the hell out of the way to give her all the room she needs.
As for the catwalk. It is pretty much a bridge with walls high enough on both sides so that the audience can't see what is on the platform. Which houses two stage hands to make sure she flys safly/ and who pull her up to the platform when she gets to the top. And the all the mechanical parts that get the flying to work. She exits on one side and there is an elvator that gets her downstairs.
"If you try to shag my husband while I am still alive, I will shove the art of motorcycle maintenance up your rancid little Cu**. That's a good dear"
Tom Stoppard's Rock N Roll