While it doesn't really say too much besides "ask someone else" here is the reply from MDC:
At no time are you allowed to venture on to private land to access a bridge or other fishing spot without landowner permission. Bridges are generally considered public access to rivers and streams. If there is an access road that leads under the bridge, and it is not marked as "no trespassing", generally you're okay. However, parking and getting access under the bridge can be a challenge sometimes. Many newer bridges no longer provide a convenient right-of-way to get under the bridge.
Safety concerns are really the biggest factor. If MoDot or the county determines that it is unsafe for the public to have access on top of or under a bridge, they can prohibit access to fishing. The same goes for parking. Some counties may not allow parking on the side of the road near a particular bridge. Again, at no time are you allowed to venture on to private land to access a bridge or other fishing spot without landowner permission.
Two things I would suggest. Contact the county assessor's office and find where the public and private land surrounding the bridge is. Then contact the Conservation Agent for that county to see if parking or fishing around that particular bridge is prohibited. You can find the county Conservation Agent on our website at http://mdc.mo.gov/node/19935.
I hope this helps,