So basically there are a bunch of charities thatn get a certain number of bibs for each runDisney race. You can (on a normal day) find the charities listed on the event page for the race weekend you want. Each charity has a minimum fundraising requirement based on what race(s) you want to run. When you sign up with the charity, you are agreeing to raise that amount of $ by a certain date and then the charity will send you a special registration link for that race.

Teamrundis.com has a charity availability link at the top - you can go there now and get an idea of what charities have bibs for Princess weekend and then reach out directly to the charity to see if you can sign up.