First off, GPS are for guidance only. If you know your prerred route, you may have to ignore the GPS for a while until it picks up on the correct route.
Does your model have a "T" in it? These models pick up traffic details. Wonder if it was erranously thinking the bridge was temporarily and routed you the quicker direction based on this info. And remember, quicker is based on distance and speed limit, not actual speed because of traffic. Sometimes, it's only a difference of 0.1 miles or 0.5 second that makes the difference.
Sometimes, when the mappers program things, they screw other things up. There is a part of road near my house that after doing an update, just disappeared. They fixed something on one of the side streets and messed up the road section. So now, when I'm headed out in a certain section it takes adds 3 miles of traffic instead of taking the shorter traffic free route.
It appears that your current map version thought the bridge (or road section) isn't there. I would recommend you
report the error to Garmin. They should look at the report to verify the map data is accurate.
You can also put you GPS in simulate mode, which should let you choose a fake start point and destination point then provide you a route. You could narrow it down to a point directly on each side of the bridge and see the route it provides.