Sperm exposed to room air on clothing, bed linens or toilet seats lose motility (the ability to swim) rapidly. Once the semen dries out, the sperms are usually dead.
If the semen is near the woman and no fertile fluid is present, they will die within a few hours outside the body. If semen is spilled on the external genitals (not in the vagina) they can swim to enter the vagina. Thus they travel from outside the body to inside.
Inside the body sperms can survive for 72 hours or more. Half of them perish in 1 to 5 hours journey inside. Note that this half is more than 60 million sperms.
That said, you should take basic caution after sex that you've cleaned up any big splashes on her or around her.