Praise be to Allah.
We put this question to Shaykh Muhammad ibn Saalih al-‘Uthaymeen, may Allaah preserve him, who replied as follows:
He should not do that, because the Bible may have an effect on the Muslim, but it seems that the Qur’aan will not have an effect on this evil person, because he is insisting that the Muslim should take the copy of the Bible. So he should not agree to that. If he goes right, then it will be for the benefit of his own self, and if he goes astray, it will be to his own loss.
Should he pretend to agree to read [the Bible], without really meaning it?
He should not agree to anything, because that will make this person feel proud. And Allaah knows best.