Three-bedroom apartments aren't exactly plentiful ... and their being zoned to a particular school lessens your options. The two schools you mention are well over an hour's distance from each other ... Bush Elementary is in The Woodlands, a suburb north of Houston, and River Oaks is in one of the most expensive areas in the city. Housing will be far more costly in the latter area, while you'll be in for a commute from The Woodlands ... and traffic is a nightmare.
You might want to contact an apartment location firm ... just Google "Apartment Locators Houston" and you'll have your choice of dozens. You've got a major decision to make. If we can be of further assistance, please get back to us here.