"To Brooklyn Bridge" is basically an ode, and awe and amazement kind of go with the territory of odes. Crane is very consciously channeling the grizzled old spirit of Walt Whitman here, specifically Whitman's poem "Crossing Brooklyn Ferry," where the 19th century poet goes into raptures about any old thing: "Oh my gosh! A seagull! A boat! WHOAAA! Look at that building!" While Whitman was trying to convince his readers that everything in the world is beautiful if you look at it the right way, Crane's awe of modern marvels like the Brooklyn Bridge is tempered by a skepticism about some of the more unsavory aspects of modern life. But even when describing an episode as disturbing as a person committing suicide, Crane still brings a certain beauty to it and sounds amazed at details like the way the person's shirt flaps in the wind. His awe and amazement are frequently expressed through soaring and Romantic language.
Crane's attitude toward the bridge is a vestige of 19th century Romanticism, and especially the idea of "natural supernaturalism," where things in nature or the ordinary world are given almost religious significance.
Hart Crane's poetic sensibility, and his attitude toward modern life, are basically a continuation of Walt Whitman's.