I always bathe first and then braid. I find it is easier to braid with a wet mane. I also use a product like quic braid to make the mane easier to work with. With a dry mane I've found you get more flyaway hairs and the braids just don't turn out as nice. I've even used a wet sponge to keep the mane wet while I braid. Plus by bathing first you make sure you have a nice clean mane to work with. Just make sure you don't put anything like Show Sheen in the mane before you braid, it will make it really slippery and hard to keep a grip on.
Here's a little guide: http://www.horsechannel.com/horse-ex...-braiding.aspx
It also says to thoroughly dampen the mane before braiding.