This should be fine. They are looking for two things with these statements:
1. The thing you did was not really all that bad (but don't say that, they need to get this on their own from the actual offense, not you downplaying it).
2. You take responsibility for whatever you did.
If you go on and on, it's just fluff and gives you more room to put your foot in your mouth. As long as you take responsibility for what you did, they don't need an extra 2 or 3 sentences of taking responsibility to believe that you actually did mature. Additionally, going on and on with dramatic statements about how it was the worst thing anyone has ever done seems very disingenuous. You need to tell them what you did and take responsibility for having done something you shouldn't have, and you've done that.
As far as using the term "bad judgment," it is an appropriate term. I think your use will be interpreted to mean that you showed poor judgment in making a choice to do something that you knew was illegal. That is an appropriate use of the phrase and correctly conveys your meaning.