Bards are great.

They're the ultimate can-do character class (other than Druid).
The most common fighting build I've seen for bards is the Swashbucker/Fencer/Duelist type. They usually wield rapiers and forego armor (except for a bucker). Max out your Dex and take the
Weapon Finesse feat to increase your to-hit for both melee and ranged attacks (provided you stick with the weapons outlined in the feat description).
Multi-classing definitely would give your character a greater focus, but you'd have to decide for yourself what that would be. Bard with a warrior class would increase your combat ability, Bard with a priest class would up your healing and defensive abilities, and Bard with a wizard class would increase your spellcasting potential.
If you go with a warrior-type, I would recommend any and all of them; Paladin (to capitolize on a high Charisma score -- but only works if your DM waives alignment restrictions), Ranger (for some free TWF or to specialize in ranged attacks), Barbarian (to up your Strength and for some Viking Skald-like flavour), or your basic Fighter (for weapon proficiencies and bonus feats).
For a priest-type, I would seriously consider Druid over Cleric, unless your party doesn't already have a Cleric. Druids have that lovely Celtic flavour that nicely accompanies the Bard class. It's important to note that Druids have proscribed weapons, so your Duelist build wouldn't work so well with this guy. But, you would have increased healing abilities, plus shapechanging, and spontaneous
animal summoning spells.
For a wizard-type, it's pretty much up in the air. Sorcerer becomes an obvious choice, again capitolizing on a high Cha score. Wizards are good if you want lots of spell choices, but I would take Sorc over Wizard. You'd get lower level spells overall, but more of them.