Basically, bard kiting on SoD is a mix between how an enchanter would charm kill and dot kiting. Your goal is to get as much aggro as possible on your target with dots and DDs while at the same time providing buffs to your pet to do extra damage in melee.
To achieve this, you will either need to snare your target or speed buff your pet. I have always felt that speed buffing your pet is the best route.
So, songs you will need to have memmed will be 2 dots, charm, haste, mez, regen as well as selos or optimally Boots of the Journey (1.5 sec casting is beneficial you will see later). Start by singling out the best possible strength pet that you can maintain charmed for a decent amount of time. You can do this by single pulling or just normal dot kiting until you have one target. Charm this. Selos and Haste playing. Pull a target with dots and send pet with "/pet taunt off". Dot kite like normal until you see the charm fade message and immediately hit a "/cmd endsong" hotkey and a Boots of the Journey hotkey (This is where the extra 1.5s is of great benefit). Use 'toggle two targets' button and retarget your old pet, recharm. Resend pet and rinse-repeat.
If you are low health or low spawn, start casting mez on your pet and right before it lands "/pet get lost" or the hotkey in the pet window.
I have found this method for soloing to be extremely fun and rewarding compared with other means of soloing.