I bought several large Baggu bags for all my purses, so if it ever rains they're protected. This is what I take to the airport with me! They're like, $6-8 & fold up so teeny tiny, even smaller than my large Longchamp Le Pliage tote and at a better price-point for dirty airport places. (Besides, I can never perfectly fold my Longchamp up as nicely as it was when I bought it...is it even possible?! Sorry, I digress!)
Going through the security screening I too put mine in the cleanest bin I can find, then nervously bite my nails and pray until I've examined it and see no harm was done. The good news is, it never has been! In the future my Keepall 50 will be heading through the belt all by its lonesome, unprotected self, but as it is vintage with a fantastic dark honey patina, I will not worry about that one. I also think travel pieces like that look a little better with some badges of courage!
On the actual plane, I keep my bags on my lap at all times, and have never had a problem with this at all. I do travel with maybe what you would call smaller bags - a Speedy 30, NF MM, and the like. I hope this doesn't sound horrifically snobbish, but I think when the flight attendants see the bag, they understand the reasoning for not placing it on the floor where there's dirt, possible spills, and the like. It also is never in other passengers' ways, so it really isn't a nuisance. However, if I ever need to...Baggu to the rescue! I would simply put it in there, knot the handles of the Baggu together, and voila! Protection!
If people give you crazy looks, so be it! I'm used to that by now, but I simply make it into a joke that the bag is like my child before having a real child. You should've seen the looks I got when I strapped my Speedy into the Matterhorn seatbelt at Disneyland. They got even more insane after I put a hoodie over it to protect it from possible water during the drops! At the end of the day, I'd rather get a few crazy stares than have a ruined bag!