I make it into a story. "This is Mr/Mrs/Miss so-and-so, X years old, with a history of a chronic AAA and diabetes and no known allergies. He/she/it was out walking today with a sudden onset of chest pain/leg pain/nausea. We did ABC. Do you have any questions about things that I may not have covered?"
Part of my ride-time is spent just writing notes - name, address, DOB, SSN, SAMPLE, OPQRST - that I can also hand to the nurse, once I've a spare minute. It is all stuff that will need to go into the chart that I write, and that also helps as a reference sheet for giving report.
And practice. Practice practice practice.