How can I comfort my spider-phobic housemate?

We are 22-year-old women. One of my housemates is terrified of spiders. Whenever there is one in her room, she commissions me to take care of it. I don’t want to kill them, so I knock them off the ceiling so she can’t see them. Even so, she can’t sleep if she knows there’s one in there.

I’ve told her that they’ll avoid beds because they’re hard to walk on, and I’ve advised the trick to name the spider after her grandma. She still can’t sleep knowing they’re there, but at least admits that her phobia is irrational.

Any tips to comfort her or help her beat her fear?