Yes, your bag is washable!
First, dump out the loose chalk and invert the lining to remove as much chalk as possible. I like to take mine outside and beat it against the grass or a rock so there’s less chalk caught in the fleece of the lining. Next just wash the bag separately on a cold, gentle machine cycle (by hand works too) and air dry.
Washing can help to smooth out the drawstring action if your cord has gotten coated with chalk during use, and of course will remove dirt from the cute print that you worked so hard to choose!
Closing the bag tightly:
Hold the drawstring enclosure fabric away from the grommet when you pull the drawstring, so that the two ends of the cord do not pinch the fabric and draw it into the grommet hole. If the fabric pulls into the grommet the bag may not close as tightly as possible and this also puts wear on the cord, causing more friction between the cord and grommet. If your cord wears out eventually, you can find tips on replacing it here.