Have you checked out the National Park Service website for BBNP?
As for flowing water and restrooms..........that limits you to Rio Grande Village campground as Cottonwood was closed as of about 3 weeks ago. The park is very busy this time of year and most of the camping spots that you are describing stay booked up, at least those that are available for reservation. Some but not all sites can be reserved in advance.
Your best bet is to get to your desired campground first thing in the morning and wait for a vacancy. By noon or later most all are taken.