Bard is a wait and see. People were saying similar things about Syndra when she first came out, but I was pretty certain there would be a day where balance just aligned in her favor, people learned how to play her and she would be really good. I was right, she was a widely played midlaner in professional play AND solo queue all last Season (until she got nerfed, but that's a different story).
Bard is in a similar situation. He's got really useful utility, but it's difficult to use. More than other champions, your allies have to be familiar with Bard's mechanics. That mega utility also eats up most of his power budget, so he has trouble trading in lane. He's not designed to sit in lane and babysit, he's designed to take control of the side of the map he is on by roaming. Unfortunately, this requires a degree of teamwork and in solo queue this falls flat because the ADC expects to be babysat, just like any other support would do. Bard is not a babysitter, he's like a friendly neighbor that stays with the kids and checks up on them to make sure they are ok, but doesn't necessarily have to stay with the kids 24/7. On top of all this, his utility is difficult to use--sort of like Janna's ult, it's easy to mess up your own team with it.
TL;DR Bard doesn't have a lot of damage because of his utility. His utility is difficult to use, and his roaming potential has trouble shining in solo queue, because it requires a higher degree of teamwork.
The good news is he is getting some buffs to his damage, among other things, which is part of his problem. I wouldn't be surprised to see him in LCS soon, maybe not until Summer Split though. His kit works well with the "support roams mid" tactic or the "support and jungler roam enemy jungle" strategy, which are fairly common with lane swaps so prevalent.