Maybe in the case of bugs, the person means "mean" as if they are bugs that bite or sting.

'Mean' is a state of being. It is rude and has the intent to offend or do harm. People usually use it in an accusatory way, like- 'oh jeff? yeah, he is always mean to me'. In your rhyme, another way to say 'mean bugs' would be 'bad bugs', 'rude bugs', 'evil bugs', or 'bully bugs'. I"m sure someone could come up with better substitutes than me.