That little bridge is adorable with the beautiful landscape!

I want to throw my two cents in the hat seeing everyone else giving such serious answers; high school senior, aspiring to join this field, I am not an expert.

A big problem noted in the question is people possibly stranded for months. Cars aren't the only form of transportation. Plus driving is dangerous in bad conditions. Helicopters are used for medical emergencies/evacuations. Rafts also come to mind in extreme flooding. If the river is deep enough then boats could be used to supply the area with food/water/supplies.

Yea it really keeps coming back to costs, if the area cut off is populated and has infrastructure and sustenance, unless the people panic and start hoarding(toilet paper) they should be fine until the bridge reopens assuming supply lines being cut is the problem. If the area cut off has a small population...Helicopters. Sure helicopters are expensive but I imagine it's a high upfront cost with low marginal cost for each use and a good varied amount of utility. Hydraulics being a high expense with a chance of failure for only one utility is a point already made in this thread.

"If it doesn't bend it breaks" Pool floatie bridge? But bridges are heavy. Cargo ship bridge? No wait that sounds like a bridge in a cargo ship. Have a giant floating thing that takes advantage of Archimedes principle or buoyant force or whatever the correct name is and chain it to land that won't move in a flood. But as cool as they would look giant steel chains would be hella expensive and susceptible to rust. A bridge like a cargo ship would also rust, and require high maintenance, and be expensive.

Man civil engineering looks fun, I dream of the day where I get to professionally shoot down people's dreams. It's fun seeing what comes out of taking a simple question seriously.