We know that Nabonidus spent ten years in Teima (Tayma) in North Arabia during his reign, so it isn't a big surprise that he left an inscription in Saudi Arabia. That said, al-Hait looks to be about 275 kilometers southeast of Tayma. I am surprised that the inscription is so far away from it.
Nabonidus does not appear in the Bible, although the story of Nebuchadnezzar's madness in Daniel 4 may be a confused legend about him. The legend appear in a form closer to historical events in the Aramaic Prayer of Nabonidus found among the Dead Sea Scrolls. For more on all of that, see here and links, here, and here.
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