There is a way to get queued for the BG and Dungeon queues at the same time. Ive only done it twice, I am not sure what conditions are meant to be followed, what I have done is:
1) Sign for Tol Barad
2) Win/lose
3) Sign for BG while in the group
4) Leave group, change spec with dual spec
5) Sign for dungeon
Right, im not sure which of these requirements are meant to be met, but this is what I have done so far, feel free to test them out, signing for BG+Dungeon at the same time is awesome as hell and has multiple uses.
SS or it didnt happen: