You might just want to give yourself a nudge and go out on short rides, even if it's round the block.
A motorbike is as safe as the rider (driver) makes it. There are very few (I can't think of one now) people who would want you to get scared on your first few trips on a bike.
My son was never scared. From the age of about 4, he was riding with me. I had to modify my foot rests so hes feet could rest on them. He loves riding now.
Everything new in life is a learning curve. Learning something new can be fun but the first step is daunting.
It's obvious that you can't dismiss that a motorbike accident makes you more vulnerable to being seriously hurt or killed. The enjoyment of riding a bike (once you are used to it and enjoy it) by far outweighs the worry of having an accident.
Set yourself a number of times. Perhaps 6 rides or 10. Perhaps put a distance limit on the trip, say 6 miles down the road to a place where you can stop to admire the view, have a drink and ride back to your house. It's not many trips and it's not to far.
If after a few tries (like 10) and you still don't like it, then I think you are firmly against bikes.
As for the man riding and you going in the car. People like you are invaluable to a biker (no wonder he makes a fuss over you). When you go to some rallies, you need a car to put the clutter to make bike riding more comfortable. While I accept it sounds like you are being used as a side hand. Many wives/partners don't want to be involved and you do. Don't feel bas. Your man is more than likely "over the moon" about you being with him when he goes out biking.