Investigative work has taken place ahead of an upgrade to the bridge, which will begin from February as part of the Midland Main Line improvement programme.
The upgrade work will see the line through Bedford electrified up to Kettering and Corby.
The bridge will be closed in both directions from 8pm on Tuesday November 28 until 6am on Wednesday November 29.
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Pedestrian access across the bridge will be maintained throughout the work and diversion signs will be in place for motorists.
Anyone wishing to find out more about the work can call the Network Rail National Helpline on 03457 11 41 41.