So did God create the universe ex nihilo in Gen 1:1, according to the Bible? What reason is there to think so?

Yes, although perhaps the text does not say so in a way that would satisfy a critical philosopher on the point. The argument, briefly stated, is theological: the first sentence of the Bible is, “In the beginning, God created the heaven and the earth.” Is there anything other than the heaven and the earth? The author doubtless did not think so; and if so, then this statement amounts to saying that God created everything there was to create. Peter in Acts 4:24 is perhaps more explicit on this point: “Lord, thou art God, which hast made heaven, and earth, and the sea, and all that is in them”. Even more pointed is a verse that Grudem rightly makes much of in this connection: “Through faith we understand that the worlds were framed by the word of God, so that things which are seen were not made of things which do appear.” (Heb. 11:3) Unless the author here is saying—as he very probably is not—that visible things are made out of invisible things, this implies that all visible things are made ex nihilo.