Getting down from the near ledge
Some methods start by getting you onto the near ledge, below the near side of the bridge. At that point you've done the difficult part because getting the rest of the way down is relatively easy (if you want it to be). You just need to move along to a place where you can let yourself drop down to be safely cushioned by one or more sloping surfaces. Crouching as you hit should help too, though it may not be needed. There are multiple options and as far as this guide is concerned, your choice doesn't affect the identity of the overall descent, it's just a variation of the ending. Your choice would have significance if you're speedrunning of course, where you'd be prepared to use a relatively risky way of getting down from the ledge if it can save you time. But that's a specialized realm of concern which this guide doesn't attempt to cover.
Two good routes
If you're heading around to the Marine area I can recommend two good routes down.
As the ledge starts to curve left, there's a place where it suddenly dips to a low point. Get to there then continue up along the rising edge. When you're near the next bend or slightly further along, turn left a little and run off, bouncing down the cliff and off the side of a huge rock at the bottom - the nearest of the two at the back of the defence position. That rock is usually so friendly that you don't even have to do a crouch, though it's probably worth doing one if you think you're coming down badly. The design of the rock does vary however. It gets randomized from among a handful of designs each time you come through a loading point, and sometimes it's a bit less forgiving than normal. Aside from that, this way down seems almost foolproof.
If you prefer, you can proceed along the edge a bit further to drop off from there instead, just as long as you end up hitting the side of the rock. It amounts to the same really; it's just that with the first version you're running off into the safe landing area (I quite like the gung-ho feel of that), while in the second it becomes more a case of dropping off into it. Either way, there's a good chance of not even taking shield damage.
You can see me getting down there in BCM12 at 2:28, in BCM13 at 0:36, in BCM27 at 2:45, and in BCM28 at 2:00. A rather older place you can see this route taken is in the GNF highlight reel (mentioned here in the HBO news), performed by ctrl at 1:12 - though the video is very low quality and unhelpfully speeded up at the start of that phase.
That was my usual way down for quite a while, but then I found another good route. Remember that dip I mentioned? Heading into that, fall off the downwards edge and let yourself be cushioned by the sloping cliff face and then the leftmost bulge of the snowy cliff base. There are nuances to this and you'll want some practice (it's not as foolproof as the earlier way), but as long as you get a good line, probably the worst you'll get is a bit of shield damage. There's a great bonus too. If you do a jump as you get to the snowy base, it gives you a kick-off which sends you shooting out across the snow quite a way. Good fun!
You can see me taking this route in BCM27 at 5:08. That was actually how I discovered it. At the time, I was just running off there on the spur of the moment and considered it a bit of a gamble. But it turned out fine, and after experimenting I realized I'd been missing a great spot. I also use this route in BCM28 at 3:55 (after making a pursuing Hunter go down first), in BCM29 at 2:50 and 5:01 (the latter with a jump at the bottom), and in both of the fast descents in BCM30 (with jumps both times).
Getting practice
If you want to practice getting down from the ledge, or explore for ways, the sensible thing to do is to get a delayed checkpoint there. You could trigger any of the three handy checkpoints I mentioned elsewhere, and keep it delayed with jumping and grenade throwing until you've got down onto the ledge. I'd advise killing nearby bridge enemies first though, else they might cause the checkpoint to continue being delayed even when you finally want it. If there's a Banshee, that'll probably need destroying too - preferably while you're still on the bridge so you can take cover!
Or here's another way of arranging things. Play through the level normally until just past the crashed Pelican, then steal the platform Banshee. Board it and trigger a checkpoint somewhere, but keep it delayed with Banshee fire until you've flown back to the ledge - or until you're on the ledge if you want (fire the fuel rod cannon to make the delay continue long enough for a dismount). Where can you trigger a checkpoint once you've got the Banshee? If you want to do it right away, it would suffice to fly low down as far as the first red light near the start of the tunnel. Beyond that, there's the tunnel checkpoint you can trigger. With both of those you'd end up with music playing. If you don't want to have music playing, go far enough through the level until music stops, then come back and delay a new tunnel checkpoint.