All you can do is to continue to love her, be patient and to work in strengthening the bond you have with her. You can use positive reinforcement techniques while working with her. Check this link and the remaining stickies at the Training and Bonding section.
Your lone budgie as well as the rest of your flock needs to be on a room where the dogs can't have access to.
Your budgie girl needs to be on a good, sturdy cage where she is unable to escape. When allowing out of cage time, the room should be bird only, no dogs allowed.