John,
1)you do not have to have your bow cased or unstrung in a vehicle.
Only for ohvs (off highway vehicles (4wheelers) you need to have the bow cased. If you just unstring it, you will get a ticket, it has to be cased on a 4 wheeler.
2)For a bike, you do not need a ohv sticker.
3)From the big game regs- It is illegal to-
2. Carry firearms (except handguns) on an OHV during deer, elk,
pronghorn antelope and bear seasons unless they are unloaded in the
chamber and magazine. Firearms (except handguns) and bows carried
on an OHV must be fully enclosed in a hard or soft case.
Scabbards or cases with open ends or sides are prohibited. This does
not apply to landowners or their agents who carry a firearm on an
OHV to take depredating wildlife on property they own or lease.
3. Hunt carelessly or discharge a firearm or release an arrow disregarding
human life or property.
4. Operate or ride a snowmobile with a firearm unless it's completely
unloaded and cased, or with a bow unless it’s unstrung or cased. Compound
bows must be cased, not unstrung.