As in any fictional story, its authors wanted a purely-fictional but appropriate and believable name, in this case based somewhere in the English Midlands.
It means simply "at the bridge over the R. Am", and follows real examples like Cambridge.
Ahhh... Wait a moment...
I beg your pardon - I'd answered that after some questions about Alton Towers etc, so was a bit parochial, but scrolling down the page I see reference to a real "Ambridge" in Pennsylvania! I imagine its own derivation is as above!
Ambridge
Dean Ambridge is 5' 10".
Ambridge Extra was created on 2011-04-05.
The scientific or taxonomic name would be Rosa'AUSwonder'.
Dean Ambridge was born on April 3, 1982, in High Wycombe, Buckinghamshire, England, UK.
The address of the Harmonie Associates is: 270 16Th St, Ambridge, PA 15003-2225
Beaver County, in Pennsylvania
Ambridge
The address of the Laughlin Memorial Free Library is: 99 Eleventh St, Ambridge, 15003 2305
The address of the Logstown Associates Historical Society is: 931 Maplewood Ave, Ambridge, PA 15003
Imelda Staunton
One for The Money