Is there any mention of a specific remembrance to be said when passing over a bridge?

No specific mention has been made for passing over a bridge. However, it is recommended for a Muslim to remember Allah Almighty by saying "Allahu Akbar" (God is the greatest) when ascending. Al-Bukhari narrated from Jabir ibn Abdullah, may Allah be pleased with them both, that: "When we ascended, we would say 'Allahu Akbar,' and when we descended, we would say 'Subhan Allah' (Glory be to Allah)." The remembrance of Allah is legislated in every pure place and in every situation, and this includes remembrance when passing over bridges.