If I'm in that situation (arriving to see a solo ref) it would depend on what I had that evening and the time before my game. If I had two varsity and the teams like to run, I may not offer because I only have so many trips up and down the floor at my advanced age.
If time constraints mean I need to change and pregame, sorry. I'm there to do a job and need to take care of my business.
However, if it is after the game I always talk to the official at the first break in action and say "You're doing a great job, do you want to finish alone or do you want some help." That puts the decision where it belongs...on the official working the game. I've offered, its your call.