After getting off to a rapid start, Asher-Smith was unable to hold off Hunt and Adeleke in the final push, but in finishing third she claimed a ninth European medal – a tally only bettered by the 10 of Polish ex-sprinter Irena Szewinska.
“Dina was not handing it to Amy. She was going to make her work hard,” former British 400m runner Allison Curbishley said on BBC Radio 5 Live.
“Asher-Smith held on as hard as she could. Then she started to over-stride, and the hips dropped.”
After finishing fifth in Monday’s 100m final, Asher-Smith returned for the 200m to continue her bid to win a historic seventh gold and become the joint-most successful athlete in the history of the championships.
But there was further disappointment for the 30-year-old, who won European 200m gold in 2016 and 2018.
“I’m disappointed to have a bronze, but I think 10 years after my first one it is such an achievement to be in a place to come back year after year,” Asher-Smith told BBC TV.
“It doesn’t matter what’s going on in my life, just come and continue to be one of the fastest women in the world. Happy to have done that today.”
Before the race, there were hopes of a British one-two-three on the podium, with Asher-Smith, Hunt and Eduan holding the three fastest times in Europe this year.
However, Eduan – who beat Hunt to win her first British title in June – finished sixth.
But Hunt’s second sprint gold continues Britain’s dominance in the sprint events in Birmingham after Romell Glave and Jeremiah Azu secured a one-two finish in the men’s 100m, while Matthew Hudson-Smith stormed to 400m victory on Wednesday.