I usually apologize right away but I admit occasionally I still sometimes try to let them wash away. I've learned through experience that it's better to own your mistakes right away - like a bandaid in a sensitive spot it's better to just rip it off and get it over with.
Admitting your mistakes right away allows the situation to be fixed before it spirals out of control or builds up more mistakes along with it plus it helps people trust you more since you're being upfront and honest.