Bulk Load Files into SQL Azure?
You are on the right track. The Bulk Copy API will work. I am using it. And it's the fastest way to import data because it uses INSERT BULK statements. Not to get confused with the BULK INSERT statement which is not supported in SQL Azure. In essence, BCP and the SqlBulkCopy API use the same method.
BCP is one way to do it.
This post explains it in three easy steps: Bulk insert with Azure SQL