I have travelled earlier with a 35B, and the way I did it, was I had it with me at all times during the flight, did not put it in the overhead compartment, so it would not get squished among other luggage. I made sure it was kept in the dustbag (to protect from any major scratches) and then in another one similar to the envirosax bag, so it has double protection from all travel hazards.
Agree with rains about the environsax - dust bag is a tad "heavy" to bring for travel IMO. Whichever handbag you use and whatever seating you're in, bring things out may not be convenient when the bag is under the seat. I'll use a "flat clutch" of folded A3 size (like Celine or Gap) to hold my passport, iPhone, tissue, candy, small makeup bag. So that when I get on the plane, I can take out the clutch with me and place my handbag on overhead compartment.