My signed Neil Gaiman bookmark has a rough timeframe! It will be given away on Tuesday the 19th, between 10am and 10pm PST. When (and how) is up to the person currently driving the bus, but I’ll post again when it happens.
There are a few different ways that items are given away during Desert Bus. The most common is a donation drive - donate a particular amount (often $5 or somewhat more) or multiples thereof, and you have a chance to win. They also sometimes ask for art, writing, or photos on a given theme.
You can find more info about Desert Bus, making donations, and all the different prizes at desertbus.org. You can also, of course, actually watch Desert Bus. I highly recommend it. ;)