Jack, the only real similarity I see is in the first line, and without any other corresponding features, that may well be coincidental. After all, in the song the girl is "standing on the bridge"; in the poem, a narrator "stands on the bridge." The meter may not mean much either: many songs use it, including, just for example, "Rolling Home." Here's a 1902 recording of the poem set to music: https://www.youtube.com/watch?v=4LvnK5TRM-Q The tune is unlike that of the song, but the date may be consistent with the song's appearance.
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