A 3 year old can bathe themselves although you should still be in the bathroom with the 3 year old to supervise the 3 year old for safety.
I never let my kids in the bathtub alone until after 5 years old just to be safe.
Some kids are ready to bathe alone by 5 but it can depend on the child.
My 5 year old had a habit of falling asleep in the bathtub so I would worry that he might drown.
Sometimes you may also need to ensure the kid takes a bath and cleans up properly.
So you may need to continue helping your child bathe until even 7 years old if the kid fakes taking a bath or refuses a bath you may need to bathe them yourself.
Always make sure the bath water is not too hot or too cold before your child gets in.