Couch produced a sensational display to score 367.70 points to finish just behind Chinese stars Ruolin Chen and Huixia Liu.
The Great Britain international had led after the first two rounds and was second going into the final dive but Liu overtook her with the last effort. Chen finished on 386.05 points and Liu 370.70.
Couch’s score in the final was almost identical to her performance in the semi-final.
The city star scored 367.60 points in her heat, with dives of 72.00, 83.20, 67.50, 72.00 and 72.80.
Couch tweeted afterwards: “So so happy… I got a BRONZE medal! Nice way to finish off in Duba.”
Her Plymouth and Great Britain team-mate Sarah Barrow missed out on making the final in Dubai.
She was drawn in a tough semi, alongside Liu, Melissa Wu, Roseline Filion, Meaghan Benfeito and Alejandra Orozco, and despite diving consistently had to settle for fifth spot with 330.60.