Like Blackhawk says, get it good and dry.
You can make a bow out of about any diameter tree if the length is there. For elm saplings, I like at least 2.5", because it will take the crown no problem, and the bow can still be 1.75" wide. 4" is even better, though. Ash, and hard maple, a little bigger is better: both are harder, stiffer woods, barely less tension strong, and honestly maple might be as strong as elm. Anything with a really high crown should just be left a tad longer.
The only time I won't harvest white woods is very early spring. I have had several elm staves, taken right as the snow melts, pop up paper thin slivers, because the porous winter growth ring has a tiny layer of nice shiny, hard looking spring growth over it. So, this paper thin new ring has nothing substantial under it, and pops. Now I cut elm from late may to january. Of course, anything you intend to chase a ring on, that goes out the window. Anything with big, fat rings, like ash often has, or diffuse porous like elm might be exempt, too.
A white wood branch or sapling should be cut, roughed out an inch thick or less, but left full width, and restrained to dry with hard clamps. Spring clamps or rubberbands won't do it. Saplings of all sorts love to warp laterally as they dry, and often twist. You can even just set it on a 2x4 and nail big nails along the sides, then bend them over. But you'll need a few. If you trim them down small enough and peel the bark, then dry them slowly (first couple of weeks) white woods won't check. Don't lean it behind the woodshed or anything.
