Two options come to mind. First, and possibly not the easiest but certainly the most direct, set up a VPN so that it's part of your network. Second, you can copy from the Azure VM to Azure Blob storage using Azure PowerShell commands. It's pretty straight forward. Then, from the local machine, you can copy from the Blob storage down and then run the restore. That'll work.
"The credit belongs to the man who is actually in the arena, whose face is marred by dust and sweat and blood"
- Theodore Roosevelt
Author of:
SQL Server Execution Plans
SQL Server Query Performance Tuning