You could try using TransMac, which has proved very popular.
The procedure is as folows:
Install TransMac and then run the program. Insert the DVD into your drive and the larger USB drive into an available port. Right-click on your DVD, select "Save Image of Disk" and save it to a folder on your hard drive. Wait for this to finish. Next, right-click on your flash drive, highlight "Format Disk" and select "Format with Disk Image". Select the DVD image you just created, "Open", and then click "Yes". Wait for this to finish, this will probably take at least half an hour.
Hope this helps!
That actually assumes you are starting from scratch, which I can now see is not what you are actually trying to do here, but I will leave the post in situ, just in case it is of some help.