Actually I'd say discretion is the better part of valor: if you dig in your heels you seem unreasonable and open yourself to eminent domain or similar.Just tell them you want 50% of what they're playing to rebuild the bridge so you can rebuild your lawn. If the bridge is $1mil than you get 500k. The cost of the bridge including surveying cost, what they pay for materials and labor, etc. Does the bridge even need replaced?
I'd probably just put up no trespassing signs and tell them to get lost if the bridge still works.
Working with the government always causes grief. Just try to make it someone else's greif and not your own.
You want to appear willing to play ball, just make it clear it's hard ball.
If it winds up in court you'll do much better as the pleading, victimized citizen than the crazy anti-gubermint loon.
Not saying it's right, just saying play your cards carefully for the best outcome.