The main problem with "bikes not allowed" is that Garmin treats cars and motorbikes as being in the same category. I am into making Garmin GPS maps and while doing so, I need to set for each component (roads, intersections, bridges, etc.) what can be done like the average speed, which categories are allowed to use it, one way sections, turn restrictions, etc. and what is not allowed.
So, if there is a fly-over or a bridge where motorbikes are not allowed, I can set "Motorbikes not allowed" but, because bikes and cars are treated the same, this will then automatically include "Cars not allowed" as well. So the only thing I can do is to set a warning message like "motorbikes not allowed" but these warning messages are not taken into account in auto-routing.
So, the best option, like Heilong asks for, is to prepare/collect a POI file of bridges, etc. where bikes are not allowed and use these while making routes.