Because Bard's such a terrible support, maybe he could prove himself in the jungle? Not really, he is clearly far from being the meta, but there some unique features in his kit that makes jungle Bard interesting, somewhat effective and fun in a whole new way.

The first thing to be careful of, as it is with all non-meta junglers, is to avoid being countered and becoming under level. The first method would be to take strange jungle paths, such as starting at the camp closer to top lane, a second would be to prioritize taking razorbacks, as they're the most common countering target. A third way, unique to Bard, would be to place shrines in buff brushes, not only to these provide effective escapes for your team, but if you're paying attention to the map, them disappearing without an ally picking them up means someone is at your camp. Also, shrines reveal their surroundings when they are placed, use this to check if camps are up, when they spawn, and because the enemy jungler is likely to destroy while they are clearing, you can use this as opportunity to ambush them.
In the first 1:55, you should drop your trinket (it's more likely that the enemy team will invade you, or even come late to catch you at low hp due to your slow clear) and dropping all three shrines. The first one would be between inner and outer, not does the mean using your W ASAP and gaining the cooldown, but it can be used by your mid in the off-chance of getting poked hard early, otherwise, you pick it up when you move to the next part of the jungle (also saving time). The other two should be places between your first two camps (even though Bard is slow, you should still start grumps/gromp, so you get their bonuses).

Furthermore, because Magical Journey doesn't help you with clearing, you can get it at level 4, and if you're feeling insecure, you can save for escaping possible counters...also I would personally use to save time and move through the jungle faster (if you didn't know this already, never smart cast it, the marker is really important for those obscurely long portals). The rest is pretty obvious: Keep autoattacking, use q on large and one small monster when it's up, and drop shrines for 10 seconds (preferably in brush to catch enemy if they come, or in the path to the next camp, to optimize time) before picking them up (unless you're about to be executed).

Because it's so difficult to actually land, Bard's Q has the best value in terms of cooldown, range and duration. This makes it more effective against monsters, as you don't have to worry about missing it.
Combined with blue, the CDR mastery, and the 20% from Magus, you can drop shrines very frequently, because it takes about 10 secs to clear a camp, you can have 2 beside towers for your allies to pick up, easily scoring assists, or saving them...it's like Soraka ults, except they are under the control of your allies, have a way low CD, give movement speed...etc.
It's a shame that Magical Journey doesn't really help you in the jungle...except for running away, it's hard to use it to save allies, as you have to be on the same side as them first (but at least you've got your W for that). And so you level it last, and because enemies can also travel through them, you're going to want to bait them in taking it, while you don't. The best way to do this is to run into a brush, drop a W for movement, to get out of vision range, and when your pursuers get into the brush, all they see is the portal, and so the logical move would to travel through it. Also, you can travel through it 10% faster, then Q them right as they get out (if they follow you).
A huge benefit to jungle Bard is that his ult would usually be used the same offensive way, as opposed to the way that messes everything up, this will be explained in the next chapter.

Bard's ganks actually aren't too bad, you can pick up a chime(s) and run into lane (after using a portal on the jutting wall, if you're feeling ballsy) with a movement speed bonus, speed up your ally, and quite easily stun the enemy champion with a nearby minion, this is already better than the ganks from most meta junglers. If they escape, you can then ult just the enemy champion and catch up, like a longer, faster Sejuani ult. You can also ult from the brush to initiate, in a way, this is the perfect gank, as you ally(ies) can position them into the optimal position, before you stun them right as they get out, before slowing while chasing them with a movement speed buff. If the gank goes wrong, you still have your E for both you and your ally to escape out of.

When not building support items, it's best to build AP on Bard (well ok, AD/DPS don't benefit him in any way, AP's the only other way), this buffs your passive, Q and greatly improves your W, giving you some burst and ability to turn a chase around after some kiting. Because defensive items don't benefit him either, you might as well go full AP and rely on your double "Zhonya's" as defense. At first I've mistaken that CDR reduces the time for Meeps to come (due to the white text), as expected, it doesn't and so, because CDR and magic pen don't do much for Bard, you're best off with tabi for jungling, you can also get mobility or swiftness, but I really dislike mobility despite its popularity; once you're combat, it's basically nonexistent, if you're a champ with movement speed buffs to make up for the movement speed lost from mobility, think of how you could've been ever faster. Mobility isn't even that great for escaping, as the enemy is aware and may be even blow summoners/ults to stop it from proccing.
While armguard is a good item to get early (because you need armor for monsters), Zhonya can come way later (you already have one, and stalling doesn't do much for Bard, esp. since he has so many escapes/cc). Lich bane, on the other hand, is really important, due to your lack of clears, and by alternating between q and w, you can proc lich bane whenever its passive is up. Also, movement speed is always good for lining up your stun, assisting, and collecting chimes.
Luden Echo's is a good item on any AP caster, even more so champs with high mobility (such as Bard), and even even more so on those without clears (such as Bard), it also really increases Bard's damage (by giving him another AP-scaling "spell" to add to his meager two, by this logic, you can also buy Nashor's, but DPS doesn't benefit him (it's still hard to clear due to his low AD/slow windup) and you already have 25% CDR from Magus/masteries.

You can always run the standard AP runes that you probably already have (magic pen reds, ap quints, armor yellows, mr/lvl glyphs), but hybrid pen reds/quints would be more effective, as Bard does a great deal of autoattacking and he doesn't deal much magic damage.

While his clears aren't too great, Bard's ganks and ability to assist all lanes (as he was intending to do, except you don't have to leave your ADC while doing so) make him a decent jungler, he can also make easy money with better/more frequently placed Ws (as opposed to support Bard) makes for easy assists, saves...etc. His spells are just more effectively used in general, your Q is easier to land, you can't really use E in lane, your W is either unused, or not effective enough to prevent your ADC from being bursted, and as mentioned before, your ult is used in a safer manner. When ganking, while he can't do much damage, he can lock down the enemy for your ally, and even if you can't get the kill, you leave your ally with more HP. In conclusion, I find jungle Bard actually more effective than support, his spells are better used (esp. his ult), and it gives players a chance to practice his unique mechanics safely (without being a useless support (you may argue that he's a useless jung instead, but when you reasonably gank, you can't do worse for your team, and his ganks are actually good)). At worst, he is just a better rivershen.