Executive summary: "Do whatever you want, just don't divert the stream flow".
Longer story: Man I love Idaho. I had some water rights paperwork I had to fill out, and rather than mailing it in, I decided to drive to the Idaho Dept of Water Resources HQ (in charge of all surface and groundwater in Idaho) in Boise and while dropping the paperwork off, take a chance on asking a gov official about the bridge thing and my water boundary in general. I went from talking to one agent to sitting in a conference room with three other people who did a whole powerpoint thing on the big screen. Apparently my particular issue was something they had discussed in a recent staff meeting. I live in what they refer to as "no man's land". I don't belong to an irrigation district, and my water is basically what they use to divert overflow from the districts back into the Boise river. They are required to keep that water flowing at all times.
Anyway, what I learned is that while I am responsible for making sure there are no blockages in the creeks, they also told me that because they are on my property, I can pretty much do what I want otherwise: fix my bridges, put new ones up, whatever. In fact their civil engineer, for erosion control on my secondary bridge, told me to just make it easy on myself and do one of the two methods mentioned here - rip rap or concrete, as that is what the state has used elsewhere. No permits required - just do it. Turned out they were jazzed to have a real world case scenario.
I asked if I had to worry about some fed.gov jackass coming out and fining me. He said they consider my area "no man's land" as well (for now, anyway) and I am well off their radar. Just as a backup, I also called the girl at NRCS who comes out to my place for habitat study, because I'm additionally removing some streamside trees that are growing at an angle and encroaching on my neighbor's water pump. Also no problem, and she in fact thanked me for doing it because the trees are Russian olives and they want them gone anyway and are asking me to plant willows in their place. She also said no problems on bridge work.
I don't think I would have gotten the same answers back in CA. Anyway, below are the images of the bridges. The first one is my main bridge, and you can see one side is pretty much all solid, while the upstream side has been going through a bit of erosion. I'm calling a civil engineer on that one. I was thinking something like rebar and concrete up to the bottom of the bridge, angled to deflect water versus taking it head on, but we'll see what the engineer says. At full flow, the water is maybe 6" over the culvert pipe (I marked high water points last season). On the second bridge, you can kinda see the lack of material high up under the steel portion of the flatbed. I plan on filling that gap with riprap and/or concrete, and bringing it down the sides to the water as well. At high water, the water is maybe a foot below the middle of the bridge. I'm thinking about maybe putting small cinderblock diversion walls at maybe a 30deg or so angle on both upstream sides to diver water from the banks there, but I'll probably drive the engineer over there as well, just to see what he thinks.