I asked my older sister who spent the majority of her job on the road, flying in airplanes and staying in hotels. Here is her reply to my query (edited slightly with her permission):
"As a woman who travels on business a lot, I pack so that I can handle my own luggage --- always. I do not want to be dependent on anyone else. I don't know the intentions of those around me. And I must be careful giving out personal information to those I sit with. (like where I'm staying when out of town). I almost NEVER give out my business card. Unless I have made a really good connection that seems appropriate (usually with a woman, however -- and usually a connection about spiritual things.)
Regarding helping women with luggage on a plane, I would not assume the woman can't heft it into the overhead. However, if you see her looking around for help, I think that's an invitation to offer assistance. Just simply ask if you can help (with a smile) and accept her response either way. It shouldn't be a personal affront if she declines. But if you've waited until she appears to want help, then do so. Men sometimes help me pull luggage down from the overhead -- probably to keep me from bonking them on the head! I just say thank you and let it go. In an airplane, you're in a "community" that disbands as soon as you get off the plane.
Common courtesy and being polite is the order of the day, in my opinion -- without expectation and without taking a rebuff personally.
Be VERY careful with women traveling alone at hotels, in hotel restaurants, etc. I do not welcome any attempts at conversation in these instances. I am perfectly content to eat alone, and usually take my iPad so as to have something to occupy my time as I wait for the meal. I am not rude; just not welcoming at all. So, I would advise against any contact. (unless she falls on the floor and you help her up, etc....but that's different.)"
From my sister's response, I have gleaned a few things that are appropriate for men who want to respect and honor women:
1. A woman who is traveling is careful about the people around her. Hence, to inquire into a woman's personal information is not wise. It may give the wrong impression. If a woman freely gives that information, she is either not too savvy about the dangers of doing so or is wanting to have a relationship that extends beyond the airplane trip.
2. It's OK to ask if a woman wants help with her luggage, especially if she is telegraphing that she wants assistance. If she says she doesn't want help, there is no need to take it personally and that she thinks I am a dirty old man.
3. Flying together in a plane is a temporary "community." It operates long enough to get to the destination. Outside of the plane, there should rarely be continued contact.
4. There is no need to be overly friendly to women that are traveling alone. But there is also no need to be rude. Just be observant and if she is in obvious distress, then offer assistance (again if she declines help, don't take it personally).
I hope that this advice helps to spur you into thinking what it means to be a gentleman. A gentleman thinks of others and is mannerly.