@lilyesh Well, I think you should apply and see what happens. I also think you might be surprised at the amount of kids who apply from your area. Many BS are filled with kids who came from public schools that were excellent ( otherwise, they would have a harder time getting the scores needed). Also people who move to areas with high performing public schools often are interested in education. Our area had many well known public schools ( nationally ranked) and still many kids went to private schools for various reasons.
While, there are many kids who repeat at BS, I don’t think it’s necessary. Many repeated because they didn’t have a great 9th grade elsewhere and wanted to start when everyone else did, many for sports ( this is most popular), some for what I’d think is academic reasons. Most of the repeats are not at the top of their class academically but everyone has a different reason. Some of the international kids were on a different timeline. No academic weakness at all. If you are strong academically and on par socially/emotionally there is no reason to repeat. My kid has classmates who came in as 10th graders and they all integrated very well. Again, it really depends on what makes you most comfortable.