I think you need to drill down more specifically with your enquiry. So far you haven’t even said whether it’s an enquiry specific to Buenos Aires or Argentina more generally.
Whilst it is likely obvious to you that there are far more bilingual schools in Buenos Aires than elsewhere in the country there are also options in other locations.
Let’s say you are interested in Buenos Aires then it’s a very big city hence a location-specific question will yield more help.
Most but by no means all of the better known bilingual schools are located in the northern reaches of Buenos Aires and indeed some of them are strictly-speaking outside of the city limits. Two very well known schools in Olivos spring to mind for example; Northlands and St Andrews Scot’s School;
So here is a question…
Does your living location drive your school choice or does your school choice drive your living location?
I think that’s a decent starting point for us to advise a little more.
Best wishes