It is on the same network and there is a network share.
I found that if I create a Text File connection I can see the mapped drives on my computer and can create connections to the files I want to import.
However, when I create a Bulk Insert task then I can only see drives on the SQL Server machine. Does this mean I have to map a drive to the server on the SQL Server machine in order to use the Bulk Insert task?
Yes , that is correct. I thought you were initially talking about being on the SQL Server machine and connecting to another server. Alternatively , can you ftp the text file onto the SQL Server machine?