After some digging, I think I have the answer.
This was known as the Providence Bridge. According to this book, it spanned a path between Sisters of Providence on the east side and St. Mary-of-the-Woods College on the west.
https://books.google.com/books?id=xvZ39oC1z6MC&pg=PA110&sour...
It was also removed in favor of a straight path across the ravine in 1989.
Incidentally...I have more bad news for you. One of those two interesting bridges in St. Mary's is now gone:
https://www.tribstar.com/news/local_news/lake-le-fer-foot-br...
No idea how far back this bridge dates, but here are some more vintage postcards that date back to the early 1900s that I managed to find while searching:
I imagine this is long gone, but there are at least two other interesting bridges in St Marys: the South Ravine Bridge and Le Fer Bridge. Both are now pedestrian bridges. I have been here several times, but not to look for bridges. This now goes on my to-do list.
Best guess on the location? Somewhere a bit northeast of the South Ravine bridge (BH 71704).