The national event was incorporated into the Trafford 10k on Sunday and the Bristol & West AC runner clocked a time of 33mins 56secs to finish runner-up behind Jess Piasecki (32:51).
Davis’ time was just 16 seconds outside her personal best set in Cardiff in March and is her third fastest ever at the distance.
“It was a tough last mile and legs were screaming to stop,” said Elsie afterwards.
“This medal was worth every step of struggle (and now) time for a short break.”
Davis, who is coached by former international Helen Clitheroe, is currently 16th in the UK Rankings and second in the South West behind Jo Pavey (33:12).
In the men’s race former B&W runner Tom Merson, who is now back with his home town club of Exmouth harriers, finished ninth in 30:37.