Just like in real life, not taking regular baths in Red Dead Redemption 2 can have negative consequences for your health - especially on Arthur Morgan's health core. On this page you can learn where you can take a bath and how much this "luxury" costs.
Arthur can take a bath in a hotel. These locations can be found in the largest towns in the game. The first hotel is in Valentine.
You need to pay for renting a room with a bath. However, this costs only 25 cents.
During a bath you can ask a woman working at a hotel to clean Morgan. This will cost you another 50 cents.
Additional note - When Arthur's hygiene level is dangerously low, he can be forced by Miss Grimshaw to take a bath - this happens when you go back to the gang hideout. She forces Arthur to wash himself. On top of that, you will also have to pay her.