I've done something really unprofessional and have been called out. Ages ago a client overheard me saying some less than unflattering things about them. Another colleague was on the phone and unbeknown to me had to put the call on hold while asking me something about this client. The client is tricky, difficult and generally annoying. This isn't an excuse, but mentioned for context.
A few days later they phoned back and mentioned to my colleague that they had overheard the conversation. Nothing more was said.
Today the client has called and spoken to me about something else. She didn't agree with the charge we are making for something. Not something I have control over and cannot be changed, it is what it is. During her first call she was fine and didn't mention the other incident. When I emailed her about the change she called back to question it and because I couldn't help/change it she then told me how rude I'd been a few months ago, calling my unprofessional and unedifying. I agree, it was out of order and I apologised, but I feel terrible.
There shouldn't be any repercussions at work as she is known to be difficult and not well liked, but I feel I need to make amends. Do I email and apologise again, or should I just leave it? Safe to say, lesson learnt and I will be making sure I don't do it again!