Step 1: Spit it Out
Ask for the help you need, short and to the point. Do so without hesitation, in a strong confident tone of voice. Do so without apology, it is to the benefit of those you serve. Do so without qualifiers. Yes, they are busy too, no need to state the obvious.
Step 2: Stop Talking
Once you make your request, stop talking in both your outside AND your inside voice. Pause, let them respond. Listen to hear. Do not be forming your rebuttal while waiting for them to speak. You will have plenty of time to navigate your next best steps once you hear what they have to say.
Step 3: Stay Focused
If they agree to your request, repeat back and clarify what you understand them to be agreeing to. “Ok”, even a “yes” is not a commitment. Be specific. If necessary, get the agreement in writing, if only in an informal email as a follow up to your conversation.
If they say “No” to your request, take a deep breath. This is no time to tuck your tail...