I would recommend using the phrase you learned in class if anything. It's not a common phrase that I tend to use but it depends on the context. I would leave out the "do" at the end and replace it with an action such as "go". You could say, "Be sure not to go out after dark." Or you could make it a command and say "don't go out after dark."

"be sure to not" is negating what ever verb will follow. "be sure to not litter" = "be sure you do not litter" But it's a weird thing to say.