What is described is a trustee-to-trustee transfer, not a direct rollover. The term "direct rollover" only applies to movement of funds to or from a qualified retirement plan like a 401(k) and no such plan is involved here.
As Carl said, make sure that the bank classifies the movement of the funds from the first IRA as a transfer and classifies the receipt of the funds by the second IRA as a transfer. Do not permit the bank to classify the movement of the funds out of the first IRA as a distribution or the deposit of the funds into the second IRA as a rollover; it is neither. Bank front-office representatives are notorious for making this mistake, so check any paperwork carefully before signing.
