Just wanted to record the results of further research. The Garmin webapp characterises cycling into a number of subtypes which are:
Three types of Cycling:  Road Cycling, Mountain Biking, Gravel/Unpaved Cycling
Three types of foot traffic: Running, Trail Running, Hiking

I repeated my test, and found that the ViaVerdi bridge will NOT route if I have selected "Road Cycling". But routes just fine if jI select "Gravel/Unpaved Cycling".

I see that the Via Verdi bridge has a dotted line on Open Cycle Map - and that is presumably seen as being unroutable for Road Cycling. 
There is merit in the Garmin classfications. But I don't understand why Open Cycle Map shows the bridge as "dotted". I am familiar with the location, went there today!, and the bridge is a low hump - with the cycle path paved the same all the way through.

Thanks.
 