Moving a washer and dryer when relocating across the country
You should use them to avoid not having any means of recompense from the shipper, or from the manufacturer by voiding the warranty.

If you didn't save yours, replacement shipping bolts can be obtained from most appliance parts suppliers (the label with your model number is probably behind the door).



I would not be concerned, if you're the one carefully putting it into a box truck and also the one taking it out (Edit: and the one doing the driving).

The shipping bolts are for keeping it in sellable condition, even after it falls off the forklift a few times.

Upon further research, the shipping bolts for a front loading washing machine keep the mounting springs from receiving excessive tension when bouncing up and down in transit. I will amend my answer by saying that if I were to be the one driving the truck, it would be fine (you may want to reconsider).