It is possible to bulk copy just the date into a datetime field. The storage size will be the same as if you had both the date and time. For a datetime column, this is 4 bytes for the number of days since January 1, 1900, and 4 bytes for the number of milliseconds after midnight on that day. If you select from SQL Server what you have input with bcp, you will see the time "12:00AM" on the end of each date, because the number of milliseconds after midnight is 0 (zero).
To display just the date portion of a DATETIME field, use the style parameter of the CONVERT() function. For example:
select convert(char(12),getdate(),3)