It won't help your score so maybe you won't feel the need to wash your golf bag as often as you do your. However, your bag is meant to protect your clubs from grime, and a carrier that has accumulated filth will do a poor job.
Start by emptying the bag completely, and don't forget the pockets. Once finished, get to work with your bristle brush, soft cloth and liquid soap around the outside and in the pockets. If you have a blemish you want to remove, turn to your go-to household stain remover. Hose down the bag and let it dry in the sun.
To restore the original shape, stuff towels in the pockets to expand the compartments.