Can anyone recommend a camping site in Northern California that has swimming as well as bathrooms?

Depends on what type of camping you are looking for also how northern Cali you are seeking. A couple off the top of my head are Lassen NP (awesome spot with hot springs, lakes, and great scenery) also in that area is lake almanor ( a very nice spot with many private run campgrounds around the lake. there are a plethora of state parks in the SF bay area, Ventanna wilderness further south by big Sur area. If you give me more detail on what type of area and space you are looking for I can give you a decent list of sites to check out. (depending on what you are looking for i can give ya a heads up on some lesser known places that rarely fill up because they are lesser known or firstcome places that are not posted on reserve america etc.

If you like the Sierra Nevada Mountains, here's a great place: GROVER HOT SPRINGS State Park, outside of Markleeville in Alpine County. Off the beaten track but definitely worth the drive. It has a swimming pool complex fed by the natural hot springs there, with pools of varying temperature from barely warm to pretty hot! Great camp site, too. The perfect family spot! Trust me! Cross-country skiing there in the winter, though the pool hours may be limited. Its best to check ahead! http://www.parks.ca.gov/?page_id=508

McArthur-Burney Falls Memorial State Park

Have you been to Whiskey town lake near Redding, Tent camping showers in the bathrooms and yes last time I was there they were clean, you can swim in the lake the water is cooler but very clear and clean...

How about one in the Napa valley with a swimming pool. It is called Napa Valley State park(boothe) and is between St Helena and Calistoga. It's very clean and you can go wine tasting, bicycling, hiking or take a mud bath in Calistoga. Very few state parks have swimming pools and this is a rare exception.