Bowstrings

Doesn't take but a couple of seconds to string the bow.
Step. Push. Loop. Done.

The string is heavily waxed, so I don't think water would be much of an issue. So long as the character takes proper care of her bow.

I've never used my bow in the rain. I don't think it would be a big issue. Can't say for sure.

I shoot a very similar bow to the one you posted in that video (not that fast though, sheesh!)

I have been told it's fine to leave strung for a day, unlike some other bow types, but personally I wouldn't be happy leaving it strung overnight. As mentioned, it only takes a matter of seconds to string because it's easy to bend and flex.

I've shot in both light rain and heavy rain with no problems on the bow, though I was careful to dry the string out flat afterwards. I would be more concerned about the arrows - the feathers get a bit waterlogged and bedraggled and I ended up sticking a plastic bag over the top of my quiver to protect them between targets. Obviously plastic bags might not be an option for your character

Hope this helps!

If they run into bandits or wolves she wouldn't have time to string an unstrung bow. By the time she had the string in hand, put one loop on the lower limb, stepped through the bow, and then went to put the other loop on the upper limb, the bandits would have attacked or the wolves would have got her.

Now, if she was carrying an unstrung bow and heard wolves in the distance, or saw smoke from a possible bandit camp, she'd have time to string the bow to get ready before moving to investigate the possible bandit camp or before the howling wolves got closer.

But, if it's happening "right now" she wouldn't have time to mess with stringing the bow.

As to keeping the bow strung all the time, yeah, if she's traveling, she'd likely keep it unstrung, especially in wet or rainy conditions. She may even have a fabric or leather cover or container for it.

She'd also likely have a spare string, and other archery kit. For arrow repair she could have spare feathers or ones that she (or someone else) already pre-cut into fletches, along with glue and thread/string to attach the fletches to a shaft. She may also have a couple spare points (arrowheads) especially if she broke any arrows earlier but was able to recover the points.

Add some beeswax for waxing the string and a small utility knife for working with the feathers, wax, etc, and she'd be pretty well set.

What's the technology?

Perhaps strings can be kept fully functional in the rain in modern times, but that was not the case in medieval times. There's the famous case of the Battle of Crecy, in 1346, when the Genoese crossbowmen were all but ineffective because their strings had become wet in the rain as they marched to the battle site.

In this case it probably comes down to what you want. If you want your character's bow to be at the ready, just work in a quick reference to waxing the string. Maybe she sees rain clouds forming. OTOH, if you want that to be a problem, make sure she acknowledges it: uh-oh, rain. I'll have to wrap up my bow to keep it dry.

The type of bow makes a great deal of difference, too. A composite bow made from pre-modern materials is nearly unusable in wet conditions due to a tendency to disintegrate. In dry conditions, though, it outshoots anything.