For the record, despite elm, with an intact growth ring, being extremely tough and really resistant to breaking, you don't see many backings made of it. And, wood backings come from perfect boards, you know?
Unlike Tim Baker I DIDN'T have particularly good results decrowning small diameter elm staves, except in some kid's bows. But, that was a long time ago. I may not have been good at it then. I'm just saying, take a long look at the board-stave, really understand the grain, then choose and trim out your rough bow carefully. Leave extra width and length, etc.
Good luck.