Well if it was me then yes I would bring a bottle of something. As you don't drink then that will work perfectly for you as you can bring something that you actually want to drink. Or you can decide to bring a bottle of wine and a bottle of something for yourself. I would do this attending any kind of BBQ unless specifically told otherwise.
For a hen party you don't need to bring anything, just yourself. You'll probably find that the chief bridesmaid (usually with the brides help) will have arranged any activities for the evening. Or in this case the food.
An appropriate time I don't know. I guess about 9pm would be ok but generally I like to see how these things pan out and go from there. If the bride is particulary wanting you to stay then it might be a bit rude to go early. I'd make a judgement on that when I'm there.
Also, and I really don't mean for this to sound critical or mean, it honestly might help. Concentrate on the fun aspects of the BBQ rather than the nightmare parts and I'm sure you'll relax more about it and have a lot more fun.