"Bare-knuckle boxing" is a term that describes both an ancestor of modern sport boxing, and any fight sport where the participants fight without benefit of glove and head protection. In most important aspects, training for bare-knuckle boxing will look a lot like training for boxing: you'll develop cardiovascular endurance, physical strength, punching power and footwork. What will be different is how much time you spend preparing your hands for the impact of unprotected punching. You can draw hand-conditioning exercises from different traditions, ranging from boxing drills to kung fu.
Do at least one round of your bag work with no gloves or hand wraps. As your hands and wrists grow accustomed to this new stress, do increasingly more of your bag work barehanded until you're working all of your rounds without protection. Canvas bags are slightly better than vinyl bags for this, as they are rougher and will build your callouses faster.
Condition your hands further by punching an old book 20 to 50 times per day. Start with a thinner paperback, then work your way up to a thick paperback (or a stack of two thin ones). Eventually work your way up to a sturdy hardback book.
Apply antibiotic ointment immediately to any scrapes or abrasions you find on your hands after a workout. This will speed the healing and avoid infections, which are a common result of scraping up your hands on a punching bag.
Ice your knuckles and wrists for 20 to 30 minutes after each workout, to ease discomfort and speed up how quickly you can get back to training.
Put bandages on any areas of your hands that need it, but only after you're done icing. Otherwise, the bandages will just fall off during icing.