We've never had any issues. I put them in while they're still quite hot and then cool them down just before I need them. I figured that keeping them hot will delay bacteria growth. I only tend to use them within a few hours anyway.
Another option is to do freshly boiled water, then put in the bottle bag. Then buy some little plastic pots and put your measure of powder in them - then you can just chuck it in the water when you need it. If we're going to be out for a long time I'll usually take 1 bottle completely made up, and a couple of bottles of hot water with little pots of powder.
If we're going to someone's house I'll use the bottle bag to transport them then put them in the fridge at the other end.