The pins idea is a good one if you have standard spots where the bridges will attach. Another is simply to have a small bump or box on either side of where the bridge will sit. That should be more than enough to keep the bridges in place and you don't have to have holes, magnets or any other sort of attachment that would be obvious when a bridge isn't there. It also would be a system that works even if the bridge is angling up or down.
Really though, I wouldn't bother. I do Necromunda with my own terrain and I much prefer the freedom of being able to place my bridges anywhere. I've never had a problem with bridges falling off. Of course most of my bridges are made from broken 0-scale gondolas so even in plastic they have a bit more weight which probably helps keep them in place. Maybe glue a few coins to the underside of your bridges to give them a bit more heft?
Here's one (two games side by side actually) of my layouts.