By now, I hope you've seen Mel Robbins' video on the word "fine". She pretty much said all there is to say about that. If you haven't watched it, it's 21 minutes well spent. Go here.
That leaves the word "busy". I really have a contentious relationship with this word. It really is an excuse. I know because I used it all the time. Next time you find yourself telling someone that you haven't been in touch for a while, instead, tell them this: YOU weren't my PRIORITY. X
Hey, I'm not saying that there aren't legitimate reasons to have other priorities. And if that's true, it shouldn't be hard to explain why you've been preoccupied.
Try this for a while. Every time you're about to say you've been busy. Say, "YOU weren't my PRIORITY.