Off at a tangent.
I recommend people not wash the inside of their bags for best practice, instead turn-out and brush, brush, brush gently instead. Most dirt is from particles and can be got out this way, applying water often makes those particles into something that can stain permanently.
I don't want to be alarmist but in a worse case scenario with some leathers, the lining is protecting the actual leather of the bag. The back (reverse) of most leather bags is actually a lot more porous than the front and will take a long time to dry out and it can harden when it does. If you have sprayed your bags and waterproofed them previously the water will have nowhere to go at all and can make the leather buckle, bubble or disintegrate.
If there's a stain already spot clean only.