A little back story, my co-worker S and I have been working together since I started at my job 3 years ago...we are friends outside of work and generally agree on most topics.
Yesterday S and I were having a discussion about upcoming work at his cubicle. We were not super loud but it was near the end of the day in a fairly empty office so it wasn't whispering either. Anyway we started talking about how my job title has changed and how it was basically thrust upon me as a take it or else scenario (ugh this is a whole other post). This new job is field work and requires working closely with construction crews...which I have done before and wasn't super fond of but its a job and well I need money...
So the topic progressed to how in the past I had some bad experiences with Hispanic workers and sexual harassment in an environment where the management did nothing about it (expect switch my shift and leave him working there as normal). Needless to say I left said job and was expressing to S my feelings about possibly being put in a similar situation again. Then we continue on to how there is a good chance that I will be working with many Hispanics and how I hope nothing bad happens. (I know maybe not the best topic but like I said we are friends and I was thinking at the time).
So I leave work yesterday everything seems fine. I come in this AM and the new(ish) receptionist that replaced me when I went into the field last year is a bit cold, doesn't say her usual good morning. Okay, so maybe its still early. Then I notice the copier needs toner and since she orders it, I ask her if we have more and she gets snippy...so I ask if everything is okay...its not.
ACTUAL IMPORTANT PART:
She asks if we can step outside to talk and I agree since I have no idea what is wrong and am thinking maybe she is having a problem with another coworker and doesn't want anyone else to hear her. She then tells me that when S and I were talking she heard me say negative things about Hispanics and "those people" and that it really upset her. I feel terrible, I start to shake a little as I am horrible with confrontations, especially when I know I fucked up. She goes on to say that she is partially Hispanic and that she is really offended but doesn't want to go to the boss about it because she is worried about her job and mine.
I apologize to her for any misunderstandings and tell her that I meant no offense to her. I say that I will not try to defend anything I said as I don't remember and that I felt that back peddling only undermines the point. Then I said that I am deeply sorry again and that I hope she and I can still work together. She half agrees and then goes back inside.
Now I feel like shit...I know I was wrong. I feel like my boss should know that this happened, but she doesn't want me to say anything. I really didn't mean to be offensive and I understand that our topic of discussion was not work-appropriate...that is most definitely a lesson learned. I don't know what else I should say or do as I feel like trying to defend myself to her will only make it worse...we haven't worked together much and I am honest and truly not a racist (as was accused) or a bad person...I just said something I shouldn't have and acknowledge that fact.
So, should I still mention this to my boss despite her wishes not to? She is still being very short and snippy, do you think it will pass? Is there anything more I should or shouldn't do?
TL/DR: I unintentionally offended a co-worker that is a different race than me while talking to someone else at work (cringe I know!) and she confronted me about it but doesn't want to involve the boss.