Getting very earthy isn't it? Follow Michael K's analogy and you wouldn't feel too keen on singing the song more than one time...

When you write a song, and feel it's a good one, you know that there is something new in the world, and it wouldn't ever have been there if you hadn't come along.

When someone asks you to sing a song, and you sing them one of yours which you've just written, you're sharing that new-thing-that-wouldn't-have-been-there-without-you with them.

And you sing it in a strange place, you know that you aren't singing the song that someone else sang just before you came in, or every week for the past year. (And if by any chance it came about that someone had just sang your song, or made a habit of singing it, that would be even better.)

And you can change it about as much as you want till it feels right without some purist coming up and saying that's not how it should be sung.(Once again, if that did happen, better still.)

And if you sing it without telling people you wrote it, it's better - then if they like it and say where did you get it, you can modestly tell them your wrote it. (If they don't like it you could always say it was Bob Dylan or someone..)