If you cut down a osage tree now (split out staves) it'll take you a couple years for it to season on it's own. Osage don't really come unto it's own to 5 years 10 years is better. Every year it's left to season it gets better.
I'm not saying you can make a bow out of 1 or 2 year old staves. You can or you can put it in a hot box to help it along. But it's best to seal the ends and let nature to it's thing.
Ok to cut your own staves is the only way I'd personally go but while there drying get you a stave of 2 to practice on.You've already been offered a stave. If all you have to do is pay S&H you better go for it.