There is another solution for this.
Consider the quotes as part of the fields delimiter, by editing the fmt file.
You can check this out for more information:
http://blogs.msdn.com/b/sqlserverfaq/archive/2010/02/04/how-to-remove-unwanted-quotation-marks-while-importing-a-data-file.aspx
An extract of the link above:
The only way to remove the quotation marks would be to modify the column delimiters specified during the import operation. The only drawback here is that if you inspect the data to be inserted, you will very quickly realize that the column delimiters are different for each column (Delimiters highlighted above).
So to specify different column delimiters for each column, you would need to use a format file if you plan to use Bulk Insert or BCP. If you generate a format file for the above table structure, it would be as follows:
9.0
3
1 SQLCHAR 0 5 "\t" 1 FName SQL_Latin1_General_CP1_CI_AS
2 SQLCHAR 0 5 "\t" 2 LName SQL_Latin1_General_CP1_CI_AS
3 SQLCHAR 0 50 "\r\n" 3 Company SQL_Latin1_General_CP1_CI_AS
Modify the format file to represent the correct column delimiters for each column. The new format file to be used will look like this:
9.0
4
1 SQLCHAR 0 0 "\"" 0 FIRST_QUOTE SQL_Latin1_General_CP1_CI_AS
2 SQLCHAR 0 5 "\",\"" 1 FNAME SQL_Latin1_General_CP1_CI_AS
3 SQLCHAR 0 5 "\",\"" 2 LNAME SQL_Latin1_General_CP1_CI_AS
4 SQLCHAR 0 50 "\"\r\n" 3 COMPANY SQL_Latin1_General_CP1_CI_AS