BCG 'may' agree to an extension, though that's not guaranteed. Note that they did feel comfortable asking me to defer my acceptance by a year a while back, so part of me would like it if you turned the table on them, ha!
Do the BCG interviews. If you do get the offer, great - but remember that statistically, you won't. Meanwhile, I suggest you accept the banking offer since that's the only job you have at the moment.
Let's assume for a moment you work in banking and now receive the offer. What to do, what to do? Yes, the experience & expertise you would develop in (investment?) banking - but that is also true to consulting. Could you get experience in both? Many people do that, typically starting IB after undergrad and MBB after MBA; the reverse can also happen, though not nearly as often (you are more likely to do MBB/Private Equity).
Ultimately, you need to decide what you really would like to do in the future. IB probably still has the edge for investment/M&A jobs, but MBB will open more doors in general - especially if you stay more than a couple of years.
I sincerely hope you get to actually face the problem. For now though, fI suggest you ocus on preparing your 1st round and don't think too far in the future. Good luck