Bach's passion is a liturgical piece. The liturgy prescribes the reading of a passage from the gospel according to Matthew as translated by Martin Luther. The words of the gospel are taken from this translation verbatim.
You can see that Luther used the word asabthani in the 1545 edition. I have not been able to find an authoritative discussion of the reasons behind the difference, but I have found several sources showing that the Greek text uses σαβαχθανί, which may be transliterated as sabachthani. The (not terribly authoritative) secondary sources that I have found agree that asabthani is Hebrew and sabachthani Aramaic. One suggests that Luther was influenced by psalm 22, the source of the phrase, which seems plausible, but I have not found anything other than speculation to explain why this might have been the case. Other explanations are possible.