If you miss your court date and there is a bench warrant put out for you and you go to turn yourself in will you get a new court date or get arrested?

Whether or not you are arrested on a bench warrant depends on the court and offense. Most courts just require another bond be posted but if the underlying offense is serious enough, or the judge is upset enough, then arrest may be inevitable -- but this is rare. I have had several cases involving bench warrants where I have just made a phone call to the court to recall the warrant and reset the court date. Of course, each case is unique.   The information provided in this answer is provided for general information only; the information provided should not be construed to be formal legal advice nor the formation of a lawyer/client relationship. It is strongly advised you contact a lawyer in your geographic area to more fully discuss the issues raised in your question.