I'm still new with bowyering, so this my answer is based on my general woodworking experience and what I've read on the subject.
Assuming you cut down the live tree it will take a while for it to air dry enough to work, I don't know how dry the wood should be for making bows, so I'd just listen to Pat and Ewok if you are going to air dry.
I do know a few kiln-less methods to speed the general wood drying process, but I'm not certain how well they will work with bow staves so use at your own risk.
One involves a microwave, so unless you have a 92" microwave, it's a moot point.
The other is to place the piece of wood in a trash bag (with the dimensions you are working with you'd probably need to cut and tape several together) lay the bag sideways on the floor and fill the bag with a decent amount of dry wood chips/shavings and saw dust. Then get some coffee filters, fill them with salt, and tie them off at the top to make pouches. Place the salt pouches at approximately equal intervals through the bag on either side of the piece of wood, and change them when they are wet. It's been awhile since I used this method, so some of the details are a little fuzzy (seal the ends or don't seal, bark on or off, etc.) But you should be able to find the details online if you want to try this method.
I've never tried it personally, or even seen it suggested as far as i can recall, but you might try putting the staves in a small room with a few dehumidifiers, or if you feel like experimenting with the theory you could even install a few outlets or run an extension cord into a hotbox and plug in some dehumidifiers. Again never tried it but I don't think it could hurt.