may be rare, but it is used.
from reputable co.uk. sites
"So the full cost of a business journey may be more or less than the expenses ... Ian purchases a train ticket for a business journey for £87."
(a gov.uk. site)
"Your business journey has many dangers, potholes and diversions but by getting your vehicle in shape and the sat nav programmed correctly ..."
"... answer your questions and help guide you through your business journey, providing timely advice on your most pressing business concerns."
"Record the mileage of each business journey in your diary or schedule, together with the reason for the trip, multiply that by the agreed rate and add it to your ..."
"Start by working out what counts as a business journey for you. Always record your business mileage – it helps with all methods. The method ..."
I think "trip" just sounds a little too colloquial in some contexts.