The belief regarding the migration from polytheism to monotheism is due to archaeology of the Canaanite region. The history of that region (and the history of the Old Testament) is a complex story, and people who were raised using the Bible as a source of history tend to be misinformed regarding the real history.
Now, I think the migration towards monotheism started in the period around which we'd place David/Solomon, but it's been a bit since I looked at that. Again, archaeology.
For textual reference, we have to remember that the Old Testament is actually a compiled series of documents, each having a different historical tradition, that was merged into one document. The wikipedia page on this is a decent starting point, though obviously you'd want to get an actual textbook or two if you're really interested in knowing your stuff.
Anyway, because there are these different sources, we can see the 'throwback' to polytheism in some of the text. Remember, the compilers of the Old Testament into the Babylonian form were obviously monotheistic. They were just honest enough as scholars to try to keep as much of the original documentation/phrasings/text as possible. They were interpreting the text as monotheistic, though.
The word 'gods' here is the same word as 'God'. It's a plural term as well as being a singular term, and you have to use context to figure out whether the author means plural or not. It's a bit like the word 'sheep'. However the (E) text periodically refers to plural gods, one of the first cropping up is that humans would become gods after eating the fruit of the tree. In fact, the gods talk amongst themselves (or God talks to the gods). Now, it's easy to back-justify as assume that it's the trinity or the 'royal we' or something like that, but to do so is an error in conceptualisation
So, when you say "Otherwise, the Bible would have said that God ruled over other gods.", you're actually correct. It's what people thought!
Not, "they're not real", but "He is above them". In the Moses part of the story, the gods are referred to, but not denied as actually existing.
It's not until later, with writings by later priests, do we see Elohim turning into a 'true' god and statements against other gods being non-existent. These passages were written during/after the Solomon era, during the push from polytheism to monotheism.
Now, if a person is just interested in proving the Bible as 'true', then what I wrote can be brushed aside. However, a person who is interested in history is encouraged to keep this idea in the back of their head, and to seek a more authoritative source than I am for more information.
He's kidding, isn't he? You don't think? 
No, he HAS to be kidding, there's just no freaking way.... 
No? 
Seriously? 
Here, 
