1- Remove all hair and dust from the rug's surface by sweeping it with a broom or vacuum cleaner. If you have an old-fashioned broom, use that instead of a regular vacuum cleaner so as not to damage the fibers in the rug.
2- Use a damp sponge dipped in mild detergent to wipe down the entire surface of the rug. Let everything soak for 10 mins before scrubbing it with a sponge, then rinse it.
3- Let everything air dry entirely before placing it back in the bathroom, as it may not get completely dried in there because of the steam.