What should I say by way of explanation/apology?

I don’t know if there is much you can do other than try not to make it worse. If she shows again, make sure you don’t repeat the act.

I can’t imagine you going up to her and saying something like, “I don’t know if you heard me joking around the other day, but if you did, I hope you didn’t get the wrong impression. You see, we sell black cherry tomatoes, as well as other kinds, and work is boring here, so I like to announce my orders in silly voices. I hope you didn’t hear that and get the wrong impression. If you did, I want to clear it up. I was just having fun. I didn’t even realize you were around until after you left. If it bothered you, I am deeply sorry. But the last thing I would ever want is to insult someone.”

But if you did want to say something, maybe you could say something along those lines. I think there are some things in life you can’t do much about, except let go. Maybe she didn’t hear you. If she did, maybe it didn’t mean anything to her. And if it did, maybe she can get beyond it somehow.

I would just drop it and hope that your friendly ways in the future make up for it.

You sound like a really great person for considering her feelings. If you happen to see her again, you could go over and say, “You know last Monday, I got in these tomato plants and when I saw them I noticed the name sounded like a soda pop I used to drink, black cherry flavor. I was kind of surprised so I blurted out the words really loudly and now that I think about it, I’m thinking that I must have sounded like some sort of a crazy person, and I hope you weren’t offended by shouting. I know it might have sounded kind of like some bad words. Please forgive me.” and give the sorry I was an ignorant fool half smile with the embarrassed furrowed brow look. Hopefully she’ll laugh and realize what happened.

You are entitled to make harmless jokes, and that one was harmless. She is entitled to be hyper sensitive and be offended. If you make some apology for your faults, she should too, for her own faults.
But if you really give a shit, why not ask her if it was problem. If she says yes, just say sorry. If she says no, just say good.

Wow, I’m a little torn here. Part of me understands how you would feel embarassed and feel like you need to apologize. The other part is telling me that you really didn’t mean any harm/harassment/bigotry so just let it go.

Answer? I can’t tell you that. You have to decide what’s right in your heart.

She obviously misinterpreted the context in which the comment was made and I agree with @Kardamom that it’s lovely you a. noticed her reaction and b. care about it.

You have a couple of options I would say. You can wait for a more natural opportunity to talk to her and if she seems ‘off’ with you, broach the subject then. Privately. You could explain you thought you saw her react but didn’t want to make matters worse by approaching her. Explain the game you all play and about the plant.

Or you can just bite the bullet and say “Hey, I think I may have upset you and I really feel bad about it” then explain what was going on. Really, she can choose to accept your explanation or decide not to. You will have done what you can do to resolve it though.

I don’t think you need to apologise at all. Your intentions were in no way offensive so if she chose to take offense then that is her problem. If your employers bring it up with you then I would tell them what you have told us and they may tell you to be a bit more discreet in front of people you don’t know in the future. Let this one go and be friendly with her in the future, you may even be able to get her in on a similar joke in the future so that she will realise that this particular time was innocent.

How did you find out that the woman took personal offense to the comment? Did she say something to you or to someone else at the company? The reason for asking is that, if she complained, the person who heard the complaint should be the one to offer the explanation. This was a misunderstanding. I see no reason for an apology. Seriously. What are you to say? You are sorry that she misinterpreted what was said?

If you sincerely didn’t do anything wrong then I wouldn’t apologize.
If she was offended, she’ll let you know. You can apologize in that case.

hmm.. You did mention that she registered a reaction. You could let her know you noticed a reaction and were hoping you didn’t offend at all. If she was offended then, sure, apologize for the offense!