So BDOC is the schoolhouse for learning specifically DIVO fundamentals and shiphandling. They are in both Norfolk and San Diego. Typically, you'll go to the site closest to where your ship is stationed at. There might be those random times where someone goes to an opposite site, for example BDOC Norfolk for a ship in SD.
SWOS in Newport, now called SWSC aka "SWO School," is the main headquarters that oversees different training sites for SWOs, enlisted Sailors, and international partners around the world and also serves as a training site for engineering, shiphandling, navigation, combat systems, etc. all taught under one roof in Newport. BDOC is a subordinate training site that reports to SWSC. Depending on how long you stay a SWO, you'll be reporting to SWSC multiple times throughout your career.
Ultimately, your PCS orders from OCS will tell you where you are going to next. Those will be released a couple weeks before you graduate OCS. From what I can recall, you'll do BDOC, a billet specialty school (if you're lucky), JOOD in Newport, then report to your ship.