Which Office are you applying to? It depends on the office
I was rejected in June 2017 by BCG and was told to reapply in 2 years. I will finish my Masters in July 2019, which will be 2 years apart from the rejection time. However, most graduates application are open in this coming September, should I apply this September?
You can call the local office and talk to HR. HR will give you the best advice on the specific dates since it's their job and they have all up to date information
I think you should apply, even if BCG is THE place you wanna work with. At the least regular real interviews uncover deeper insights into our strengths.
As other suggested, I would strongly suggest to apply but to have conversations with recruiting before submitting your application online so they know it’s coming and why you apply now and flag it appropriately so it doesn’t get discarded automatically.
hope it helps,
In addition to the above, I would also suggest networking and trying to get a referral. Check the alumni network for your Master's program or any friends and family.
I personally worked with someone who was rejected and then applied the following year through a referral and got the job. He as a great consultant too!