Flying Lawyer,
While maybe not considered reckless by the CFR you gave, we have to contend with the separate item:
91.13 Careless or reckless operation.
(a) Aircraft operations for the purpose of air navigation. No person may operate an aircraft in a careless or reckless manner so as to endanger the life or property of another.
(b) Aircraft operations other than for the purpose of air navigation. No person may operate an aircraft, other than for the purpose of air navigation, on any part of the surface of an airport used by aircraft for air commerce (including areas used by those aircraft for receiving or discharging persons or cargo), in a careless or reckless manner so as to endanger the life or property of another.
This gives the FAA the right to add that, when they cant hit you with any other regulation in an enforcement action.
My take on this is for that bridge, likely nothing would be said.
However for myself, it is not something that I might do, not so much for the danger to the bridge, I discount that, but more to the unknowns to myself and the aircraft.
The what if's of a possible wire hanging from it, or something falling from it as I pass under, or (far fetched but who knows) if someone decided, seeing my approach, to try throwing something down for a rotor kill as I pass under, lot of strange people out there...