A simple way would be to add a default constraint to the RecordDate column on the table before each bulk insert is executed (or modify the existing constraint, if there is one). Each inserted row will pick up the default for the RecordDate column (obviously assuming the row doesn't contain a value getting imported into RecordDate). Remove the constraint after the bulk insert is completed.
alter table <Table Name>
add constraint <constraint name>
default <relevant date here> for [RecordDate]
<run the bulk insert...>
alter table <Table Name>
drop constraint <Constraint Name>