According to http://www.rits.org/www/structures/rigone.html The Rock Island trackage between Mercer and Mill Grove (16 miles) was realigned in 1946 to what it is today, to reduce curves and grades). Depending on how old this postcard is, and it looks to me like it dates prior to the 1940's, this would have been along the old alignment. Checking on Google Earth, there is a street on the south side of Princeton that crossed the tracks in a cut, at the appropriate spot in a bend, and that is S. Coleman St (which runs perpendicular to the tracks, at the crest of the hill). About three-quarters of a mile south of there is where the new line diverges off the old right of way and heads to the east. I'll buzz up that way tomorrow and snoop around to see if my suspicion is correct, and post some pics, if I can get any.
I believe that this is the bridge that used to be off Hwy 65 west of Ravanna, Missouri.
It was destroyed many years ago and I do not know if it was replaced.
If you took the road west from the well in Ravanna, it would eventually cross the railroad track on a bridge and connect with Hwy 64.
The 1046 Princeton quad shows the RR grade with the road crossing. The 1984 quad shows fill across the cut. I would assume there will be no remaining evidence of a bridge above ground.
The cut in the photo looks similar in depth to the one in the location on the map. If this is the location then the photo is looking to the north.