There are a bunch of ways to move a database into Azure and you don't have to use Management Studio for all of them. The method within SSMS is to create a BACPAC which is a DACPAC plus an extract of all your data. You can then use that to recreate your database in Azure. Just make sure you're not using any functionality that's not yet supported in Azure v12. Also, be aware, a DACPAC is not encrypted, regardless of the state of your database, so treat it accordingly.
If you do want to use SSMS, I'd strongly suggest getting the new, independent, SSMS install. It has more functionality specific to Azure and will make your work easier. It is a preview release though. Something to be aware of.