Spiders don’t use doors. They are liquid sneaking machines that can flatten themselves to the thickness of a credit card. Check your window seals. If you can see daylight squiggling through a crack, a spider can walk through it doing a gymnastics routine. Use caulk—the magical toothpaste for adults—to seal gaps around baseboards and window frames. A tiny tube costs five bucks and will prevent 90% of arachnid intrusions.
Also, check your door sweep. That rubber strip at the bottom of your door? If it’s torn or missing, you might as well hang a sign that says: “Spider Welcome Mat.” Replace it. The difference between a sealed room and a spider-infested one is often a quarter-inch of rubber.