I'm a Bard Main, but it's taken me a long time to feel like I'm good at him. This is my advice:
Early game, he has insanely powerful poke, especially with the addition of thunderlord's. Landing Q + Meeps AA will not only proc thunderolord's all the way, but will proc spellthief's 3 times and chunk for a surprising amount of damage. You need to be careful, because he's extremely squishy in response to the damage he doles out, but equal trades become favorable if the enemy has no sustain, because you do.
In the laning phase, his chimes are a huge advantage because they each restore 12% of mana. No other support can restore mana. Don't run too far to collect, and always leave your ADC shrines, but those things can be useful for staying in lane longer and harassing more. Never grab a chime with full mana; pop a shrine down wherever you are. It'll get used eventually.
Mid game, his pattern shifts to roaming. His mobility boost from his chimes is amazing for getting to other lanes quickly, and a well timed ult sets up ganks like no other. Likewise, he sets up ganks in the jungle or in certain lane areas extremely well using his tunnels; ping your allies near where you're going to create the tunnel, and use it to cut off enemy champions. Pop a W on a high value target: the movespeed boost helps substantially and it's the most reliable way to get assists, which are actually not terribly easy to come by as bard.
Bard also has extreme strength in his ability to place wards. He can not only do it more quickly, but tunnels can get you out of almost anything. Just roam within tunnel range of allies, throw one down and slam a Q into the enemy while they're still in the tunnel, so they are stunned when they emerge. You can bait people with tunnels quite well (side note; NEVER ENTER BARD'S TUNNEL IF YOU'RE ON THE ENEMY TEAM. DONT DO IT!).
Late game, his pattern shifts to straight utility and zone control. His ult may seem useless, but the more you play him, the more you see its power. Time it right, you can nab 3 people on the enemy team and turn the fight into a 2v5 for a few moments, forcing people to either die or drain offensive spells. Even isolating one person can be huge; slam the ult into the frontline so your damage can kill the backline, or slam it into the backline so that they're useless for a few seconds. Also (and I can't stress this enough) keep using shrines. While you're gathering for a teamfight, throw them down in possible escape routes, you'll be surprised at how useful they are.
I like to build bard a bit unorthodox; I go for frostqueens and ignore ruby sightstone, just grabbing the regular. Then I build Ludens into Lichbane. The added AP really makes the heals and poke powerful, but it's a squishy build, so it takes care to work properly. Even with those items, a Q + AA will chunk squishies for half of their hp (I'm really not exaggerating there, it's quite nice). In games where my team needs me tankier, I go for ruby sightstone earlier, then grab either frozen heart or gauntlet (depending on gold advantage) then spirit visage or legion, all depending on what the enemy teamcomp looks like and what defensive stats I need. If the team needs more utility, I'll pick up Zeke's for the adc (usually don't do this because Bard roams too much for it to be optimal) and banner of command, or even ardent censure sometimes (so I can buff adcs with my heal). Ultimitely, bard can build whatever the crap he wants, tbh. Straight AP actually works well; he scales extremely well even though his numbers don't seem to suggest it. If you set up three shrines, you're healing for an AP ratio of 1.8 in burst, which is insane (not to mention you can throw another shrine under people while 3 are active, healing for a net of 2.1 AP).
Bard's Q is definitely a mindgame spell. It gets really, really good in teamfights, where there's chaos and more targets, but it works well in lane. Mastering his Q is the first step to becoming a good bard player; it's not quite like other skill shots. Don't feel pressured to use it only for the stun; the slow is pretty darn powerful too, and it does great damage on its own. Remember that dead turrets are still terrain (people forget that all the time) and that your actual target can be the second one you want to hit (so if someone's standing behind a minion, hit the minion and then them with the skill shot, and they'll get stunned). It's also easy to land when people chase you, and insanely easy to land when people run through your tunnels.
Bard's ult is the hardest part about his kit. Using it effectively is really, really, really, really difficult, but the power is amazing. It can be used as great engage, disengage, and it really remolds a teamfight. Just take care, the spell takes longer the further away you cast it; try to use it up close. ALso try to pick fights in the jungle: bard works WAY better there. There's more terrain to Q and make tunnels with, there's smaller gaps which makes his ult exponentially harder to dodge, and there's generally more chimes to work with. Chimes last for 10 minutes, if you have them in useful positions, leave them there so you can use them to run.
Hope some of this is useful.
