Don't adhere strictly to what Cowlitz says. The ULTIMATE decision rests with your DMV (MVD). Check YOUR state's requirements and GET THEM IN WRITING. There is no need to go to the added expense of getting a Class B CDL if your state does NOT require it. What you will ultimately have to do, though, is to thoroughly familiarize yourself with driving a larger vehicle, sometimes with different steering geometry, and with driving a vehicle equipped with air brakes. Air brakes DO handle differently than hydraulic brakes.
And, yes, do get travel insurance for this new beast, should you desire to purchase it. If you're involved in an accident without it, your fault, their fault, nobody's fault, you WILL pay dearly.