Ian Edward's 225 Year history of the club contains a photo of this bridge dated 1896. According to the text it cost £15 to build and paint. Quite a sum for the time I would have thought.
At that time, late 1890's, the 16th, 17th and 18th holes all played generally in the same directions as they presently do, however, the 16th was 302 yds and called 'The Mount', the 17th was 302 yds and, interestingly, called 'The Redan' whilst the 18th ('Home hole')
was 328 yds.
Things changed in the late 1920's though, when the course was changed and extended quite radically, ie the 16th and 18th were extended and the 17th became a par-3. I have no more info about RAGC's former 17th 'Redan' hole however, so don't ask!
atb