You can apologize, sure, but in that situation I would absolutely judge you strongly for it regardless. Forever or until you proved you grew out of that kind of bullshit.
I never said I'd bully anyone but I would absolutely remember behavior like that. You don't get to act like a bigot and then just say you're sorry. This isn't christianity where everyone has to be forgiven no matter how shitty they are. This is real life where your words and actions have consequences.
Nah, we'll just disagree. The apology is you doing what you think you need to do to make it right or get out of a situation. What you said or did at first would be what you believed at the time. Immediately apologizing shows no growth at all.