Do you have any shredded cheese? add a very small amount to it, and mix well. THat will thicken it.
Have you tried just heating it in a pan over low heat for awhile to simmer away the excess liquid? If you don't have any other thickening materials, this will work just as well. Just stir occasionally so it doesn't stick.
And to the responder above, it is highly unlikely that Europeans would appreciate the Hispanic influence associated with nachos and nacho dip in the US, considering our proximity to Mexico. But then, we've never cultivated a taste for Bangers and Mash or pickled herring, either!
if you have oil and eg yolk, add them and whisk til it is emulsified- which means that the oil and egg yolk thicken naturally and become glossy. It will make a nice nacho cheese dip and by thicker.
Don't think it is nasty to put egg yolk in nacho cheese dip, you already would have used flour! I am a bit confused how you made it watery- it doesn't have water in it...
If no egg yolk you can try - arrowroot, mayonnaise, more cheese, or if you have a potato, dice it up and boil til it's soft, then mash it to a puree, really puree, and add that. It doesn't really affect the flavour too much, you'd think it, but it tastes good to make a sauce thicker.
I'd go for the potato if you have one. Or the egg yolk method.
Might I venture this moment to say that nacho cheese dip is completely revolting, nothing to do with actual cheese, and would get you beaten up if you presented it at a party in Europe?