If you have the chops to improvise both foundation and fills while maintaining a steady beat, here's a few I've done myself at one time or another:
- Fever (Peggy Lee/The McCoys)
- So Much In Love (Tymes)
- Fire & Rain (James Taylor)
- The Longest Time (Billy Joel)
- Isle of Hope, Isle of Tears (Brendan Graham/Sean Keane/Ronan Tynan/Celtic Woman)
- Get Together (Youngbloods)
- My Girl (Temptations - keep the guitar riff going throughout)
- That Same Old Obsession (Gordon Lightfoot)
- King of the Road (Roger Miller)
- Come Together (Beatles)
- Can't Help Falling in Love with You (Elvis Presley)
IME old vaudeville songs with either a strong 1-5 beat or walking bass line (
Bill Bailey, Sunny Side of the Street, Sweet Georgia Brown, etc.) also work well with solo vocals/bass...