there's no way you are going to fit into a medium bambino with a 48" waist. I can only just get the lower tapes to get to the front, and I have a 40" waist. Bambino are known for fitting about a half size smaller than many others.
I'd suggest you look into recouping your losses. You will have ZERO chance of returning diapers if they are opened. I don't know if they'll take back an unopened case. You'd have to pay shipping. (and then shipping again to get the replacements sent out)
Your most economical solution right now is to find someone locally that will give you close to your cost for them. But that's rarely an option.
But bambino has shown surprisingly generous customer service in the past. It's definitely worth giving them a call or email to discuss your mistake. They may work with you a bit, especially if this is your first order with them. They live on their return customers. There may be other cost-saving options, like refusing delivery. If the carrier doesn't charge bambino for return shipping, refusing the order would get them returned back to bambino at no charge to either of you. Then all you'd be on the hook for is paying for shipping the replacement case, plus whatever the med/lg cost difference is. Again, call them asap.
Bambino are known for fitting about a half size smaller than many others.