There are no assigned bus times. NCL does not "put you on a bus". Transfer buses are first-come-first-serve.
All ashore is about 9:30 am, so they will be looking to kick you off the ship at that time. Room service is fine, but your room steward and butler really want you out of the room so they can turn it over for the next cruise that will board at 11:00 am. 8:00 a.m. is the published "get out, your cruise is over" time. (Maybe for an extra $100 tip each, your room steward and butler will allow you to stay a bit longer 😃).
The concierge staff will escort you down the crew elevator as far as the Haven/Priority line to the ship's security checkpoint, after which you are on your own. Last year, the ship's facial recognition scan was also the CBP scan and there was no stopping once we got into the baggage hall. But getting through security (after the concierge dropped us off) to the gangway and into the terminal took a [long] while.
After getting through the terminal and through the baggage hall, you will join a long like to board for the transfer buses. They have space to load a couple of buses at the same time, but it is slow, and they will try to fill every bus up.
1:16 pm departure is an Early Departure as far as NCL is concerned. You would get an 8:00 bag pick-up by default as a Haven guest. If you were in steerage, you would get an 8:15 bag pick-up time for your 1:16 pm flight time. That 8:15 recognizes that the transfer process is slow and mitigates the risk of the transfer delays causing you to miss your flight.
The 8:00-9:30 timeframe is when the line for the transfer buses will snake from buses back into the terminal and back into baggage hall. You can expect a 30+ minute wait in line to get onto a bus. Personally, even with Port Valet, I would not "play chicken" with the transfer line. I would enjoy a breakfast and move on to getting to the airport.
The existence of Port Valet is somewhat irrelevant except for needing to drop your bags with your airlines. Pre-check at SEATAC moves pretty fast. I have had a lot more delays in Miami TSA lately.
Example schedule from last year.