Advisor walked in while I was complaining about her; How can I minimize the damage to our relationship?

From what you have said, I am not sure even if she heard you. All you need to do for now is to STOP this attitude. You will never find a perfect supervisor... Yes, you can talk with a friend about how difficult your life is with this supervisor. But this should be out of the lab and avoid -- as much as you can -- other students with the same supervisor.

• Show her that you value her research and expertise (in case you don't value her research, then find another supervisor).

• Do not talk about anything happened unless she started the talk.

I completely disagree with @Penguin_Knight on the gift thing. Being so nice in a typical meeting indicates something weird is happening. Do not do it. (I believe this is a cultural thing some people may see it really good others will think about it in a very bad context.)

If you have an issue with your advisor you should approach her about it in private, calmly, clearly, and with an open mind and an idea of what you want. If you choose to speak to others without approaching her then you cannot be surprised at unexpected consequences.

As for the current situation; if your advisor definitely heard you, then apologizing to her in person, privately, would be the honorable course of action. Of course, if there's a chance she did not hear you, this would not turn out well for you.

So, I recommend that you simply approach her with your concerns as you originally should have (and do it soon, because if she did hear you, the longer you wait the more permanent the damage may become). Also make sure you have a clear idea of what you want to get out of the conversation ahead of time. This is a reasonable approach whether she heard you or not. If she didn't hear you, then this brings your concerns to light in a mature manner. If she did hear you, this opens up the potential for a conversation about the incident. If she chooses not to mention it, at least you approached her with your concerns and gave her an opportunity to legitimately hear where you were coming from.

Also, whether she heard you or not, don't simply pretend that this situation didn't happen; go into it with the mindset of "yes, it did happen, and that means it's time to have a real conversation about the issues that have been bothering me before the tension gets even worse".

Do not grovel, this only shows that you do not feel comfortable with your ability to handle confrontation, and raises many red flags (too many to list) and defenses (even subconsciously) to the person you are groveling to (one of the worst cases being that the recipient takes it as "I can't believe you think I'm so foolish as to fall for your grovelling" and thus fails to reciprocate any respect).

Do not be close-minded or have a "putting your foot down" or "shoot first ask questions later" attitude, this will normally put somebody on the defensive immediately and kill most chances of progress. Be calm, clear, and treat her with the same amount of decency and respect that you would expect from anybody else -- even if you strongly disagree with her behavior. Going into these kinds of things with a clear head (and a clear goal) will also help give you confidence that can keep you from getting on the defensive and closing doors / burning bridges.

And most importantly, do not forget that you may not get what you want out of this conversation; but at least you will end up doing your best to be reasonable and work with the situation. The relationship may not be perfect, but it is there and it is up to you to make the best of it.

I completely agree with Jason C's answer. If you are sure that your advisor has heard you, then a sincere apology would work best. Something similar happened with me long ago, and I scheduled a meeting with the offended colleague early next morning, before anyone else was in the office. My apology was sincere and she immediately understood that I had no problem with her on a personal level, just that I had a problem with her working style. She did make an effort to change her style as she realized it was inconveniencing me. We had a fabulous relationship afterwards and never mentioned that incident again. But I definitely learnt a lesson: when you have a problem, discuss it with the person concerned and not with anyone else.