Here is the item again:
Professor Neal loves chocolate cake.
(A) But could
not accept the slice that her student Michael
offered (B)
because she knew that it was a
bribe (C)
for a better grade on his midterm essay.
You correctly realized that the period after cake creates a problem. But could not accept the slice ... is a lonely verb fragment. When you attach a phrase of this type to the end of a main clause, you need no punctuation.
To fix the problem, you chose to do this:
Professor Neal loves chocolate cake but could
not accept the slice that her student Michael offered because she knew that
it was a bribe for a better grade on his midterm essay.
You have correctly employed Punctuation Rule 8:
Main Clause + Ø + Lonely Verb Phrase.
What an intelligent decision!