All schools are private here

They are run along three lines: religions, openbare (non-faith, open to all), or teaching methods (Jenaplan, Montessori, etc) and all are publically funded so are free-of-charge to parents. And they are all Dutch speaking.
There are state-
subsidised (is this what you mean?) schools that teach in English, and you are looking at around €3000 per child per year. There are also non-subsidised schools (these tend to follow their own country's system, eg American, Japanese, English, French, etc), - these cost around €12-15000 per child per year.
http://www.sio.nl/listofprimaryschools.html - this lists both subsidised and independent schools.
There is also
this school in Delft, a University town just north of Rotterdam, which one of our old forum members posted about. All public transport is regular and efficient here, so reaching Rotterdam itself would be no problem, but I don't live in South Holland so can't advise on which are the best areas.