No, Bhishma didn't make such vow to make Lord Krishna to pick up arms. Instead Bhishma made a vow to cause heavy damage to Pandavas. It is mentioned in Mahabharata, Bhishma Parva, SECTION LVIII.
Hearing these words, Bhishma, laughing repeatedly, and turning up his eyes in wrath, said to thy son, 'Many a time, O king, have I said unto thee words worthy of thy acceptance and fraught with thy good. The Pandavas are incapable of being vanquished in battle by the very gods with Vasava amongst them. That, however, which my aged self is capable of doing, I will do to the extent of my power, O best of kings, in this battle. Witness it now with thy kinsmen. Today, in the very sight of all, alone I shall check the sons of Pandu at the head of their troops and with all their kinsfolk.'