Only wash your beauty bag when it is visibly dirty. In this case, you can rub the dirty area with a clean cloth, a little water and soap. Dry it away from direct sunlight.
However, be careful with the leather part, which should not come into contact with too much water. Genuine leather can leave traces of colour when it is wet.
You can treat the leather part of your new makeup bag with a protective spray that prevents dirt and moisture from seeping into the leather. You can regularly moisturise the leather part of your bag with a leather treatment product to keep it looking like new as long as possible.