Wild ass guess: it's hyponatremia. If you're going to drink that much water, you HAVE TO use electrolytes, too. I maybe have a glass of juice or something with breakfast before a ride that short, and probably drink 1 bottle, maybe 1-/2 bottles during, then maybe finish that bottle when I get back. So try this: on the bike, only drink if you are thirsty. It's called "drink to thirst." We get thirsty because our DNA is set up to tell us when to drink, lucky us. Not thirsty, no need to drink. You'll notice that if you take electrolytes, they'll make you thirsty or at least thirstier.

I've been massively dehydrated, never made me dizzy.