Congrats on the BCG offer. Reference checks at this stage are usually just a formality, not a fresh test.
What your referees will be asked. How long they worked with you and in what role. Your strengths and where you can grow. How you handled pressure or hard situations. How you worked in a team. Would they hire you or work with you again.
If a referee says something a bit negative, it usually does not kill the offer. BCG knows no one is perfect. They look for patterns across many people. A soft comment like "could be more bold" is fine. Strong red flags like honesty issues, poor work, or not being reliable are different and can cause concern.
What to do. Pick your referees with care. Choose people who really like your work. Brief them before the call on the role and what to highlight. Avoid anyone you have tension with.
Don't stress about this. Most checks just confirm what BCG already thinks.
Good luck.