Do I need a script, or can I improvise on camera?

Yes, you need a four-line script, with what is seen, what is said and what is asked at the end. Improvising only fits an atmosphere shot where price and booking do not have to be named. Write those four lines on the phone before the camera comes out of the pocket. The price is improvised on camera and the number said is not this week’s. Each planned reel has its slip: frame, line, close, and who appears.