Nice looking snake
The aspen being a bit damp won't hurt anything, so long as it's not constantly damp/wet. You want the humidity in the tank to stay about 50-60%. Putting cling-wrap or a damp towel over about half the top of the tank will help keeping the humidity constant.
Also, if you don't want to spray the aspen, a humid hide (hide filled with damp sphagnum moss) is a good idea.
As to telling whether she's stressed; a hiding BP is a happy BP. Do you have multiple snug hides (One on the warm side and one on the cool side)? If not, place the two hides in there and she'll probably find one and hide under it until it's feeding time.
As far as handling, leave her completely alone for a week aside from tank maintenance. Let her settle in before handling her.
Sometimes if their last shed wasn't perfect they'll have little patches of skin that flake off after the main shed. I feel like that's probably what you're seeing. Nothing to worry about though (if they have a humid hide or shed box they'll usually get those off on their own)
As for a vet visit, I don't. Usually I just do a 90 quarantine/observational period for my new snakes. If no health issues crop up, they can come into the reptile room. If you don't have any other snakes, I'd recommend just keeping a close eye on her for a couple months.
EDIT: Just saw that you said you had heating pads. Do you have them on thermostats? If not, that is important because they can easily get hot enough to burn a BP. Hot spot shouldn't stray far above 90 F.