The youngster, who has been a regular in Saints' age group teams this season, kicked two conversions and a penalty at Twickenham.
But while NSB won plenty of plaudits for their tenacity, determination, invention and wit with ball in hand, up front Dulwich had too much power and their three tries from the forwards proved to be the difference.
Nevertheless Bullivant was proud of the effort of the first state school to reach the showcase occasion in four years.
"All in all I'm really proud of the boys," he told the Chronicle and Echo. "The fight they've put in and the tackles they made.
"We've got the likes of Tom Hammersley, who is 15. He's played his heart out for the side as has Roti (Rotimi Segun). They're playing beyond their years and captured all of what we're about. They never gave up.
"At the end of the day we gave all our effort to try to stop them, but they were just too big.
"We tried to play our rugby, we tried to play a little bit, but unfortunately on the day it just didn't work out for us."
Both of the NSB tries came from flanker Oliver Hartfield, and he took time to thank the support the team received from across the county.
"We had a lot of support here from the whole of Northamptonshire," he said. "The likes of the Saints have been a real support, they've all said good luck, put stuff on Twitter and Facebook and did a video for us.
"There were so many people in the town getting behind us. The sound of the crowd out there was amazing. You could hear it on the pitch - it was great support."
Earlier in the day there was success for Buckingham's Royal Latin School, who beat Felsted 19-13 in the Under-15s Vase Final.
Prop Joe Robey's late try sealed the win for Royal Latin, adding to earlier scores from wing Sam Burgin and lock Elliot Pittwood and two conversions from fly half Will Hughes.