If mice are a problem - aren't they always? - why sow them direct into the soil? I sow mine in modules (Oct 10th, last year) and plant them out when they're 3 or 4 inches high (Oct 29th). They're now 9 or 12 inches high and seem quite bonny.
Last year my first picking was May 4th (from over-wintered Aqualdulce) and then the main-crop came in from June 3rd (HDRA's heritage Crimson-flowered beans - sown in modules during Feb and planted out Feb 21st & Mar 2nd). I made the last picking of the main-crop on July 14th, the day before the French beans started!!