If you're looking for the lyrics to old broadside ballads and folk songs (or if you just want to go to a website that still has a .midi file playing in the background), this is a very good resource, organized thematically:
http://www.contemplator.com/folk.html
Some of them might not fit the campaign's atmosphere very well, but, even if you don't know the melodies, most of them are pretty easy to fake (or you could pick up a few Smithsonian Folkways albums, which are almost always worth it, anyway).
Public libraries usually have a few cassette tapes or CDs of Irish/Celtic type music (of sharply varying quality) that you could borrow from.
Testament's definitely got an interesting idea with the war and period songs; there's a 2-CD set of the popular music of WWI which I've never listened to, but you could at least find the track list on Amazon and then google the lyrics (it seems to have all the standards). There's also a series of CDs with the songs of the early 20th century (check on Amazon for "Waitin on the Levee" to see one of the series).
In addition to Bob Dylan, a lot of the Band's music has a sort of timeless quality that I could see working.
The 2E Bard's handbook had a whopping four sample songs for bard's to sing, including "The Skye Boat Song" and "The Minstrel Boy," both eminently appropriate.
And as some have noted, it can be fun to either invent or pull songs from other sources to cast your spells and bard abilties. (Elan the Order of the Stick bard is a good example of how to do this in an incredibly annoying and ineffective way ("Move, move, move, silently down the corridor!!"))
If you've got some small portable music-playing device, a good throwaway gag for your bard is saying "I Inspire Allies" and turn on "Eye of the Tiger."