There are (or were) 4 major ways to kite as a bard:
Melee - This is exactly what it sounds like. You debuff and slow the mob if you can (not until you get those songs obviously) and use your melee songs to go toe to toe with the mob. This works fine in the lower levels. In the higher levels, this is mostly limited to mobs that are mezzable. Our tanking abilities go way south as we gain levels, and need to take mez/heal breaks in the middle of combat. This can be started at level 1.
Chant kiting - This is where you use your chants (single target DoTs, one for fire, cold, disease and poison resist checks, and one for magic that generally does less damage then the others). Simply, you run in a circle playing selos and your chants on the mob until it dies. If it's a runner, you switch to snare when it starts to run. Pretty basic kiting really. This can't really be done until the 30s (?), whenever you start getting chants. You can use your DD song, but that's SLOW.
Charm kiting - This is when you charm one mob and sic it on another. Most bards will also play chants on the target mob to help it die faster, and to get full experience for the kill (charmed mobs take a portion of the experience for the kill, depending on how much damage you do vs. it). If your chants are creating a lot of aggro, you may need to run with selos while you do this and the pet whacks at the mobs back, just like necro aggro kiting. Remember to recharm when it wears off, and always recharm the same mob. Never charm one mob, then a different one when it wears off. It will ruin your aggro control abilities, which is very important when you get to swarm kiting. This can be started as soon as you get your first charm, 29 I think?
Swarm kiting - It's related to charm kiting. Think of it as "reverse" charm kiting. The goal is to grab a mob that is social (you can get aggro from his buddies just by being aggroed with him) and round up a bunch of his friends. Charm mob A and sic it on one of his buddies. They'll all start attacking him (because they're social). When he starts to get low on health, you break charm (either through invis or dispell magic) and chant him down. You'll get 100% of the experience from the kill, even though you only did 5-10% of the work. This takes practice, and timing is essential. Once you get it down though, it's EASY. This can be started when you get your first charm too, but it's VERY short duration, so it can be tough. Also, it's better to start with charm kiting so you can figure out the aggro situation.
AE kiting - This is probably what you remember seeing, the bards wiping out zones and such. I won't go into too much detail, since it has been taken out of the game (for the most part). Our AEs are point blank AEs (PBAE). They radiate out from us and hit an unlimited number of mobs, but have a very short radius (just larger then melee range in some cases). Since we can run and cast at the same time though, we were able to run in very small circles, keeping a WHOLE bunch of mobs stacked on top of each other and just out of melee range, but just in song range, and hit them all at once with our PBAE DoTs. The DoTs themselves did very little damage, but when multiplied by many many mobs, it gave us SICK DPS.
That's the basics on bard kiting. I could go into much more detail on each one, but I'll leave that to when you ask.