I just use a generic, large S&W shooting bag. Its saving grace is that it was very inexpensive while being fairly well made. It's functional but not optimal. I use it to carry everything except rifles. And ammo -- that's what ammo cans are for.
Here are the features I would like to have, and will require in my next range bag.
1) Somewhere between 5 and 8 pockets of varying sizes to store stuff like tools, oil, first aid kit, hand towel, recoil shield, etc. Also one large pocket for empty brass.
2) A light-colored interior that will reflect light. I HATE hunting around in a black bag for something, you need a damn flashlight to find what you're looking for even in broad daylight.
3) A nice heavy duty shoulder strap. This can make the difference between one trip to the car and two trips.
4) I'd prefer either no logo on it, or one easily removed / covered. Low profile.
The Gatemouth bags are nice but their interior pockets are pretty tiny.