I’ve got a Coach pouch bag that’s leather, and things spill. I’ve soaked the bag in soapy water, mushed it around, rinsed it and hung it to dry. Voila–great results.
Take it to Nordstrom. They might clean it for you, or they have a cleaning product you can buy that conditions and cleans the bag. If you have some deep cleaning, its best to take it to a professional.