It's impossible to positively identify the spider without looking at it more closely--tiny structures--eye arrangement, genitalia, etc.,--are all used to ID the genus and species.  However, this is most likely a giant house spider, frequently found in Washington homes.  It appears to be a female.  The only dangerous spider we have in our neck of the woods is the black widow spider, and this is definitely not a widow.  Even the hobo spider, a relative of the house spider, is no more dangerous than the giant house spider.

In general, spiders are not aggressive and do not bite unless they feel threatened, and even then might not inject venom.  Many of the smaller spiders' fangs can't even penetrate flesh.  However, a spider bite can cause a mildly painful skin reaction in most people, and a more heightened reaction if the person is especially sensitive.  I personally don't handle spiders without protection.

Do they like to crawl into sheets and pillowcases?  They just look for places where they can do what they do best--look for insects to eat in your house.  They might occasionally wander into places like bedding. Remember--they are in your home because there is food there, and they are performing a valuable service to you.  

Indoor spiders are specially adapted to the inside of homes, and you aren't doing them a favor if you put them outdoors.

Read more about them here: https://pubs.extension.wsu.edu/common-spiders-of-washington-replaces-eb1548