Although there are many negators in Chinese, they each have different usages. Bu不 is used in state, present event and future event, for example,「他不高」「他不在這裡」「他明天不會去上學」. Bu 不usually shows the subjective thought by the speaker. Bu不can also form different sentence structure.
E.g. subject + bu不+ verb + object「我不去上學了」
Subject + bu不+preposition「他不在這裡」
Mei沒 and meiyou沒有 are used to negate a complete event, similar to did not. However, mei沒 cannot serve the same usage as meiyou沒有 in existential sentences. It is because the word you有 functions as the predicate of an existential sentence (Sun, 2006). In「他沒有很多時間」, while mei沒 is the negator, the you有 is the predicate, similar to have in English. If meiyou沒有 is replaced by mei沒, 「他沒很多衣服」 will become “he (negator) many clothes”, missing the predicate you有 (have) to indicate the state. Mei沒usually shows the objective fact.
Lastly, bie別 is mostly used in unrealized situations to stop someone from doing something. For example, 「別拍照」.
Chinese learners have to first memorize each negators and their usage, then think about the state and time of the event in their sentences which they are trying to deliver, in order to use these negators correctly.
Sun, C. (2006). Chinese: A Linguistic Introduction. In xiv+234pp, UK: Cambridge U Press, 2006. Cambridge University Press. https://doi.org/10.1017/CBO9780511755019