A couple of comments, being someone who almost got trapped out in the Wild River Valley due to high water after 4" of overnight rain...
There are two bridges I've physically seen - the big suspension bridge way back at the start of the Highwater Trail (right at the start of Wild River Road), and Spider Bridge where the Black Angel Trail crosses the Highwater and Wild River trails. The maps and other posters here note another suspension bridge right near the campground leading to the Moriah Brook Trail.
The brooks are not bridged. Cypress Brook and Spruce Brook definitely have the size and capacity to be impassable at times of high water, the latter making the "Highwater Trail" a misnomer.
And finally, the first thing the Wild River Trail does when leaving the campground is make an unbridged stream crossing. It's a rock-step normally, a waist-deep ford at high water.
So enough of the warnings. You can read the whole story
here if you want to. The plusses are:
The Wild River Valley is incredibly gorgeous.
The Wild River Campground is a fantastic location, first-come-first-served (no reservations) with a number of great sites all maintained with an on-site caretaker.
The Wild River, at low water, is a gem to go out and sit on a rock and soak your feet in.