Ah! OK!You can dunk in RIT dye, no salt, and not super hot water. It does dry it out a lot. I doubt you will get a nice dark black. It will probably just be gray. If you really want to dye the inside to match the outside, you should probably paint it on, not dunk. If you decide to use suede dye instead, I don't recommend Fiebings. The time I tried that, the color disappeared as soon as I brushed the suede, whether I waited a week or a month. That's when I switched to painting RIT on. If you use the liquid variety, it is easier.
No, I did not encounter dye transfer to the items inside. I did do another dunk of the bag after the dye had cured for 3 weeks. The water was the color of the dye but the color did not fade- inside or out. I have not had dye transfer on items that went inside the bag. Granted, I do not put white items in my bag, nor pens. I hate pens! They always manage to leave a skid mark despite caps.
Always buy a dye that includes suede.
Also, after you dye, you may notice an iridescent look on the leather. Don't panic! Once you put conditioner on and buff, that will disappear. I wish someone told me that before I panicked.