Typically a wipe down of the exterior with regular use of an enzymatic cleaner keeps the bag both clean and sanitized. Never wash a bag in the washer, the enzymatic is actually more effective for sanitizing.
I do highly recommend to use either washable or disposable gel pee pads in conjunction with carriers, as they soak up liquids in seconds and keep both pets and carriers dry. I sell them on my site that are well regarded but any pee pad is better than none.
As far as the pad, do remove t