'Bossy' means that one is acting in an arrogant manner, more of a caricature of a boss, acting like people should do what they suggest (when in fact they do not have 'boss' status). (which is to say a bossy boss is probably not a likeable boss, but you should probably do what they say. a bossy person who is not your boss is just annoying).
The word 'bossy' is a little informal, but it has the same taboo status as, say, 'fat'. That means it doesn't have any taboo status as is, but if you call someone that, or refer to someone as that and they hear it, it is usually in a negative direction. The word is most appropriate to describe a situation where one person, who is a colleague, makes a suggestion (or more than one) in an expectant manner.
Also, in the past 10-15 years or so (probably longer), its use in the US at least has become somewhat problematic as it has accrued a nuance of disparagement particularly against women. That is, when used for a woman, it has the feeling that for the supposed exact same characteristics a man would be called 'having leadership qualities'. Using 'bossy' likely shows a double standard. Other examples might be a man called 'headstrong' but a woman 'bitchy'.
It would not be as disparaging currently to call a man 'bossy' because it wouldn't have the double standard overtones. But for a woman it is (certainly nowadays) considered disparaging.
Just as the word 'fat' has no taboo (unlike 'bitch' or 'shit'), 'bossy' has no taboo, but you're advised in US culture not to call someone fat or bossy to their face. Well, that's a little too flat. 'Bossy' is a tiny bit taboo.
In non-native contexts, saying 'you should never use this word' is a bit strong. There are similar words, like 'hysterical' or 'shrill' or 'spinster', which have both a female and disparaging connotation and may be taken badly. You probably shouldn't be using any of these words for a woman, but they're not nearly words that would be bleeped out/censored in the media.