Janisport makes a small bag called "half pint," but I always had to clip the zipper. Otherwise, if I didn't zip it ALL the way, it has a tendancy to open as you walk and everything falls out.
I have a better one that is Dickies brand, But I haven't seen them again since I bought it.
Both of the above come in black, so DH doesn't mind taking a turn carrying either. I usually only bring a bag if it's going to rain/we need ponchos and jackets.
Otherwise, as I've said many times, I usually try to avoid having a bag at all.
Cargo shorts/pants: My true favorite is to limit our stuff to what we can hold in our pockets. Mens' cargo shorts can often hold quite a bit. Look for pockets with secure closures. DH has several where the lower pocket can hold up to two bottles of water! I also try to wear a women's version most days. Not a cute as a skirt, but easy at WDW.
You could alslo try a small one pouch cross body bag. If it's got a long strap, and you can carry it across your body then you won't have to worry about losing it. If it's small enough, then you don't have to do much with it on rides. Lots of folks swear by Baggallini cross body bags.
I've also used the inexpensive nylon bags. They work, but the cords can get tiresome all day, unless the content are light. (not so great if you planon carrying six bottles of water, but fine for a windbreaker.)
The other thing is to keep your stuff light. If you won't use 8oz. of suntan lotion, dont' carry it. Carry 1oz. in a tiny bottle. If rain is only about 50% chance, sub plastic poncho for a full jacket. REstock somethign like wipes every night. If you go back mid-day, and don't think you'll need the camera at night, skip it.