I was in Edinburgh for the first weekend of this April, and with the Sunday free decided to take the short trip out to visit the Forth Bridge. A cooperative effort between local government groups runs a circular walk, the Forth Bridges Trail, between Dalmeny and North Queensferry stations (on either side of the bridge), so I took the train from Edinburgh Waverley to Dalmeny and followed the trail, taking from about 9.30 in the morning to 1.30 in the afternoon (longer than I expected, but then I did dawdle).
Apart from a slight hiccup finding the start of the trail, it's mostly well-signposted throughout, with an online map and closer-scale maps at each point. The weather was warm and sunny almost the whole way, showing off the Firth of Forth gloriously (it is a beautiful body of water), and South Queensferry (the settlement south of the Firth, where Dalmeny station is) in particular is a sweet village, which I greatly enjoyed wandering through and reading the information boards. They mostly relate to the history and construction of the Forth Bridge - the trail includes a memorial to those who died during its construction - with a little entertaining local colour thrown in, and some detail on the other bridges across the Firth (the 20th century Forth Road Bridge and the 21st century Queensferry Crossing - obviously outside of the remit of the WHS). There are plenty of views of the Bridge from various angles along the way, and the trail leads to an elevated viewpoint at the south end of the road bridge, which is home to a UNESCO plaque.
Crossing the road bridge on foot gives you a full side view of the Forth Bridge, and an appreciation of quite how long it is, but it can be rather cold and windy, and offers little else in the way of a scenic vista. The North Queensferry side of the trail gives a closer look at the bridge's structure (including a picnic area directly beneath the bridge!) but (though perhaps I was just trailed out by then) I found it the less interesting side, and not much at all was open at that time on a Sunday. In hindsight I wouldn't have lost too much by heading down to the Battery Park picnic spot and then walking uphill through the town to the station, without worrying about the stops thereabouts.
Finally I took the train across from North Queensferry to Dalmeny and back into Edinburgh - crossing the Bridge doesn't take long but being enveloped by the red steelwork does give you a sense of the scale, and you get a brief but clear view of the island below.
The trail is enjoyable, and I'd recommend at least doing the South Queensferry part of it. I was blessed with good weather (in fact I discovered afterwards that I should have worn sunscreen) - in the rain it would have been somewhat drearier.