Can I apply poison to arrows or bolts during downtime, so I do not have to waste standard actions to do it during combat?
According to the poison rules, 'A poisoned weapon or object retains its poison until the weapon scores a hit or the object is touched (unless the poison is wiped off before a target comes in contact with it).' So I would say yes, you can do it during downtime. Just don't touch it in the meantime.
It'd be reasonable to think it might lose potency after a while, but I'm unaware of any rules to that effect. There are some for losing potency if you harvested them from a creature, but it seems like once you've crafted it into a poison it will stay potent essentially forever.