This should answer your questions!
Additionally, if you want your little girl to bond with you, the best chance of that is if she remains a single budgie. Keep in mind that single budgies must have a "flock" which will consist of you and your family, so ensure you spend plenty of time with her throughout the day or she will be lonely.
I am strongly bonded to my little girl and she feels like she's part of the flock over here.
Keep in mind that not all birds are "people birds" and may be best suited to a life with other birds. If this is the case, you'll notice that even after a year of getting to know her she isn't very active or interested in interacting with you. If she seems, however, like she's settling in just fine, playing with her toys, etc. then she'll likely be fine as a single bird