Using your terminology I need to leave promptly , you need a prearranged taxi, friend to drive you, or blue shuttle (after all no one knows where you are going to and I assume it might be a train, bus, or airport).This is my help from Washington, D.C. United States of America. Please pick an answer as the best answer, even if it is not mine.
You can preplanned your pick up from most taxi company.I use red top taxi co. 703-522-3333Are you going to stay in dc or are you going to virginia/ maryland?It does matter. Use yellow pages to find the appropriate cab co.You are taking chances hailing a cab at 4am.
Call ahead of time to ensure their prompt arrival.
Your best bet is to call one at 3 am.