You can create a temp table variable and insert the data into it, then insert the data into your actual table by selecting it from the temp table.
declare @TableVar table
(
firstCol varchar(50) NOT NULL,
secondCol varchar(50) NOT NULL
)
BULK INSERT @TableVar FROM 'PathToCSVFile' WITH (FIELDTERMINATOR = ',', ROWTERMINATOR = '\n')
GO
INSERT INTO dbo.ExistingTable
(
firstCol,
secondCol
)
SELECT firstCol,
secondCol
FROM @TableVar
GO