I have both of the bags that have been discussed at length (The Lowepro LensTrekker 600AWII and the Gura Gear Battaflae 32L). Although I do not have a 500/f4 I do have the 200-400/f4 which is about the same length as the 500/f4.
The Lowepro bag is definitely bulker than the Gura gear and is a couple of inches taller since it was meant to be able to hold a 600mm w/body attached or an 800mm by itself. It is also much thicker in padding than the Gura Gear (actually the padding seems like overkill to me). You can add Lowepro S&F attachments although that does make the bag even bulkier. It does come with a great tripod support system. All in all I only use it if I am only taking one body and the 200-400 with me.
The Gura Gear Battaflae 32L is amazing. It is lightweight (Feels like it is half the weight of the Lowepro). You can have the body attached to a 500mm or the 200-400mm and it will fit in one side( although not with the TC attached). I don't fly with bodies attached to lens but it is an easy mod to the bag to have the body attached to the lens when you are out shooting.
I have not flown with it, but I have flown with an F-Stop Loka which is dimensionally bigger than the Gura Gear. I had no issues flying with the F-stop so the Gura Gear should be fine. I have had 33 pounds in my Battaflae for 6 hours hiking around the San Diego Safari Park and while I was tired at the end of the day I was not sore at all. The bag is very well balanced and sits with the weight on your hips. The ability to open only half the bag to get some gear out is a wonderful feature. The only improvement to me would be some thicker material covering the bottom so it protects the bag when you put it on the ground. They provide a rain cover which is supposed to double as a ground cover but I don't always take the time to get it out.