What happens to the mind if it gets enlightened when I die? That depends on the level of enlightenment, according to the scriptures - I don't know. According to the scriptures there are four levels of enlightenment: stream-entry, once-returner, non-returner and fully enlightened. Apparently if you become a stream-enterer you have, according to the scriptures, no more than seven more rebirths as a human being before you can get fully enlightened. As a once-returner you come back as a human being one more time. Non-returner never comes back to the human realm, it goes to the realm of the non-returners, where one gets enlightened. And fully enlightened does not get reborn in this cycle. So depending on the level of enlightenment, that would be what will happen.
"What if that doesn't happen?" I don't know but according to the scriptures seven more rebirths is apparently what happens. "Would this mean that you can't be a Bodhisattva anymore?" Yes, that is correct, according to the teachings because you became enlightened under another Buddha's teaching you are bound for enlightenment, and one of the requirements for being a bodhisattva is that you not be even partly enlightened yet. If you are a stream-enterer, once-returner, or non-returner you can't vow to be a Buddha anymore because you are already partly enlightened. All this is according to the scriptures.