The best gear tote for the playa is one that can carry your water, some sunscreen, your lights, a snack, goggles, sunglasses, a beverage or food container lip balm and anything else you might need out there while still being comfortable and not too bulky. I use a hydro-pack because the primary thing I need to carry on the playa is water. My hydro-pack is neon green and originally purchased for backpacking and S&R work. Some people like lots of pockets, other people loath them. It depends on what you are carrying and the ease with which you want to retrieve it.
If there is a style of bag you currently prefer to use, such as a backpack or a messenger bag or a purse, then try riding a bike with your preferred tote/bag, if you find that it's not working, then find one that'll work better. Burning Man sees a lot of bike and foot travel, and it's huge.
Carrying enough water to get you through the day can be really heavy. Add to that your sunscreen and various snacks you can easily reach 10-15 lbs just in gear. Because of this, I personally tend to go for back packs/hydro packs because it evenly distributes the weight over my shoulders and generally they're padded and designed for carrying that kind of weight. Another bag that's great for biking is a messenger bag. I used a Chrome Metro my first year, but its tough to get your water bottle out while you're riding unless you have it in a cage on your bike, and then, it's easy to forget your water bottle on your bike or have it fall out when you ride over some washboard.
Fanny packs: Some of them have external pockets (Like Mountain smith) that you can stick water bottles in. These are great for drinking on the go, whether you're riding your bike or walking and they don't stress your shoulders. If you're wearing one while climbing though, your water bottles can fall out. I saw this happen in 2011 at the Thunderdome, and it was a full clean canteen. It fell from way up top. If it had hit someone in the head, that was a medevac right there.
So there really isn't any holy grail of playa bags (yet) it all comes down to personal preference. Trying out a whole bunch before you go to TBTITD might help you find which one works best for you.
That which does not kill you makes you stranger.