Yes, it is recommended that a bathmat should be cleaned at least once a week, and possibly more frequently depending how often it is used, and how many people use the home bathtub or shower enclosure.
When left untended to, bathmats can be susceptible to a build-up of bacteria in the form of mould and mildew, as their location renders them unable to properly circulate air or dry off effectively.
For more information, take a look at our blog, The Importance Of Cleaning Bathmats.