Joey D’Antoni recommends backing up database to Blob Storage via URL in Azure:
Unlike in your on-premises environment, where you might have up to a 32 Gbps fibre channel connection to your storage array and then a separate 10 Gbps connection to the file share where you write your SQL Server backups, in the cloud you have a single connection to both storage and the rest of the network. That single connection is metered and correlates to the size (and $$$) of your VM. So bandwidth is somewhat sacred, since backups and normal storage traffic go over the same limited tunnel. This doesn’t mean you can’t have good storage performance, it just means you have to think about things. In the case of the customer I mentioned, they were saturating their network pipe, by writing backups to the file system, and then having the Azure backup service backup their VM, they were saturating their pipe and making regular SQL Server I/Os wait.
Read on to see what the alternative is.