Create a good lead. Even if it's only on one string, you can make a catchy hook that will work as an intro and an interlude. You'll have to slide up and down the fretboard, but you can make it work.
Concentrate on rhythm. You're not going to be able to play full chords, so you'll need to make the most of the notes you can play. The rests between the will really make the notes themselves stand out.
Use percussion! Knock on your guitar, stomp your feet or click your pick against your pick guard to accentuate the spaces between notes as you play. This can help fill holes in your song put there by a lack of strings.
Spend time on the vocal melody. If you write some catchy lyrics and a good vocal melody, the notes on your guitar will act more as a guide rather than a driving force. A great example of this is Gwen Stefani's "Holla Back Girl." During most of the choruses, there are only drums playing plus a bass tone that gets dropped once every other measure. Most of it is pure vocal melody.
Study other one-string songs for inspiration and ideas. Some popular guitar leads that can be done on one string include "Iron Man," "Seven Nation Army" and "Louie Louie." You can't play them in their entirety on one string, but these will give you some good ideas for leads and get your creative juices flowing.