The 17-year-old finished fifth representing Great Britain at the Swiss Women’s International in Bern.
Bryson was just eight points off winning a medal in the competition that attracted competitors from all around the world.
The city athlete finished top of the riding event, was ranked second in the fencing and fifth in the combined run and shoot. It was just her swim that cost her a medal. Bryson’s overall total was 1258 points.
Italy’s Aurora Rognetti won the title with 1293 points, with Britain’s Eilidh Prise and Joanna Muir taking second and third.
Prise scored 1287 points, with Muir, who won the title in 2015, collecting 1266.
Fellow Brit, Charlie Follett, 18, who like Bryson was making her senior international debut, was 13th with 1121 points.