I feel that Big D is in all honest truth Buckethead's wife. She first appears and is noted as "Big D" in the PBS Soundstage video, as she hands Bucket his 'chuks, shortly after leaving the stage. On 7/16/2011, at the Anaheim
House Of Blues, during an untitled song, a woman with strikingly similar features comes on stage and dances dressed as some sort of deer.
First off, Anaheim is were Buckethead supposedly lives when he isn't on the road, hinting that he lives in Anaheim, and that on the local tour date, his wife came on stage to dance for him.
Secondly, Big D (http://people.tribe.net/bigd
go here for her profile), is some sort of a fashion model, and the Big D in the profile looks exactly like this "Deer Lady" dancing to the ballad. Also to tie in with that, in her profile, it mentions that she is in a relationship, and MOST importantly, she states that she is "Bucketheads right hand coop buddy".
Go here for the Untitled Ballad with the supposed Big D dancing: http://www.youtube.com/watch?v=ZV9XCHPLztg
Hope I was convincing, have a good day and a happy Thanksgiving.