It is very important for a Bat Mitzvah student, and her parents/guardians, to understand that learning a first portion does not happen in a week or two. There are many things that affect how quickly a portion can be learned.
I have found that in the beginning, the very least amount of preparation for a first portion is six months if the Hebrew letters and syllables are being taught at the same time. This can be very stressful. I highly recommend the Hebrew language reading basics be finished first.
If the Hebrew is already learned, the music part can be finished in about eight to twelve weeks, depending on the length of the verses. Another two weeks is needed to practice, polish, memorize, and just simply gain confidence. Another two weeks is needed to not have to worry about it except to practice it once or twice a day while running around taking care of other important last minute details for the service. That could be up to four months!
All of that said, for young students learning during the Summer months, with no school, clubs, leagues, etc, it can go much more quickly.
Additionally, there is usually at least one dress rehearsal, if not two, in the week or two before the service. All of the blessing, parading, dressing, raising, etc. is gone through. By that time, the portion itself should not be needing any fine tuning.
That means that I recommend a minimum of three months for a Bat Mitzvah. I have seen girls do it in less, but they were not happy campers. If you want it to be fun, and something they might like to continue in the future, allow the time for it!
However, the great thing about Torah portions, is that the more of them you do, the easier and faster you can learn them. Because of the nature of the tunes and patterns, as you learn the symbols and tunes, they become a part of you. The Hebrew also gets more familiar and easier to read and learn.
The second portion goes quite a bit faster than the first. The third portion much faster than that. People who sing Torah regularly can learn a portion in just a few days. There are some who can even be called on the morning of a portion and fill in for someone sick or otherwise missing the service! I will admit, that would not be me. My music is good enough-my Hebrew is not-yet!
Note: I will not create recordings for a 1st aliyah less than twelve weeks away. That is two weeks for delivery, and ten weeks for learning, IF you already know the basics of reading Hebrew. Eight weeks is the absolute minimum for a beginner, if the portion is short. Ten to twelve weeks are better.