Ok... I got it... it was much simpler than I thought, but I didn't have any
experience on that matters before.
The answer is to use typed datasets instead of the standard dataset object.

So here goes the solution for anyone else trying it:
First you create a new dataset (add new item - dataset) and add it to your
web service.
Then you drop the table from your database tha you want to use onto the
dataset designer so now you have your typed dataset.
Then you drop a dataset from the toolbox to your web service design view and
choose the typed dataset you have created, from the drop down list.
Finally, in your function that does the reading from the database, replace
the dataset object to your new object. Here is an example:

// PhoneNumbers is my typed dataset
public PhoneNumbers phoneNumbers1;

  [WebMethod(Description = "The Phonenumbers Table")]
  public PhoneNumbers GetPhoneNumbers()
  {
       OleDbConnection myConnection;
       OleDbDataAdapter myDataAdapter;
       PhoneNumbers myDataSet;

       myConnection = new
OleDbConnection("PROVIDER=Microsoft.Jet.OLEDB.4.0;DATA Source=" +
        Server.MapPath("/") + "\\PhoneNumbers\\PhoneNumbers.mdb");

       myDataAdapter = new OleDbDataAdapter("SELECT * FROM PhoneNumbers",
myConnection);
       myDataSet = new PhoneNumbers();

       phoneNumbers1 = new PhoneNumbers();

     // you dont have to do both... you either return it from this function
or use the public object!

      myDataAdapter.Fill(myDataSet, "PhoneNumbers");
      myDataAdapter.Fill(phoneNumbers1, "PhoneNumbers");

      return myDataSet;
  }