Is it possible to bulk insert data into a table that has columns encrypted with Always Encrypted?
Bulk Insert operations in the manner you are describing are not supported for encrypted column via SSMS.

Please refer to this (https://blogs.msdn.microsoft.com/sqlsecurity/2015/07/28/encrypting-existing-data-with-always-encrypted/) article to migrate your existing data to Always Encrypted

Also, please note that doing bulk inserts through a C# (.NET 4.6.1+ client) app is supported.

You can do this in c# using SqlBulkCopy specifically using SqlBulkCopy.WriteToServer(IDataReader) Method. I am assuming you are trying to load data from csv file to a table with encrypted column (say encryptedTable). I would do the following


Create a new table (say unencryptedTable, for security purposes, you might consider creating this table in a local sql server instance) with the same schema without any column encryption.
Load the csv data into unencryptedTable, using the method that you described in the question
Do select * from unencryptedTable to load the data in a SqlDataReader then use SqlBulkCopy to load it to the encryptedTable using SqlBulkCopy.WriteToServer(IDataReader) Method


If you have additional questions regarding this, please post questions in the comment section and I will try my best to address them :)