The bridge is a wooden single lane bridge, but I have seen many big coaches staying at the lower campground across the bridge. There is an upper campground that is more wooded where I stayed a couple of years ago in my 5th wheel when I PCS'd back to Campbell. There is a way around the bridge by taking Jordan Springs and approaching the bridge from the other direction, but I wouldn't worry about it.
There is another option at 830 Tiny Town rd. I believe it's called Tiny Town TV Park. I've seen quite a few nice rigs parked there for extended time, but looks to be many open pads right now. It is not too far off Tiny Town, so there would be road noise, but more convenient for shopping and it is close to gate 3. Forgot to add their number is 931-217-3363.
Good luck with your trip.