The rule for Interdiction (23.4.4) states:
If a Strike achieves a successful result on the Interdiction Strike Table, the hex is considered interdicted. Any unit moving through that hex pays an additional +1 or +2 MPs. In addition, no road movement is allowed into, through, or out of the hex. A unit which begins ground movement in an interdicted hex must pay the additional movement cost to leave the hex.
In the terrain description for rivers it also states:
Where roads/highways cross the river hexsides, a Bridge is assumed to exist. Bridges negate the additional MPs for crossing river hexsides.
By both these rules it seems that while a road may cross a river hex-side, doing so does not require 'road movement'. Therefore interdicting a bridge can't really be done (ie, make you opponent take the +2 move for crossing a river along with the other penalties for interdiction). Does that ring true?
Hmmm...I can see an argument either way, but I'd have to say that no road movement in, through, or out means you can't use the bridge either.