You can map from the source table to the destination table with a
DataTableMapping. (and optionally a set of DataColumnMapping 's).

The source table is the table the data has come FROM, which I presume exists
in a database that is accessible only on the server side. This table name is
contained in the dataset.

The destination table is where you want the data to go, which is MS Access.

This example shows how to copy data from one database to another using a
single dataset, and a DataTableMapping.
http://www.winisp.net/cheeso/srcview.aspx?dir=misc&file=copydata.cs

The difference for you is,
 - you obtain the dataset from a webservice, not directly from a database.
 - you are copying into a MS Access db, not a SQL Server db.  This means
you will need to use a OleDbDataAdapter, not a SqlDataAdapter (but you
already knew that)

you can also check the reference page
http://msdn.microsoft.com/library/default.asp?url=/library/en-us/cpref/html/frlr
fsystemdatacommondataadapterclasstablemappingstopic.asp

Couple other comments:
 - I am pretty sure your UpdateCommand should not be a SELECT.  It should
probably be an INSERT or UPDATE.
 - You will need to actually update each row in the dataset if you want the
UpdateCommand to be applied.  See the example given above.

-D