Reports are not my strong suit...but you may be able to use the On_Open Event (or maybe the On_Format Event) of the form to hide/show the result textbox depending on how many records are in the row source.
Something like:
Code:
If DCount("*","SourceTableOrQueryNameHere") >=1 then
Me.txtSumTotalTextBoxNameHere.Visible = True
Else
Me.txtSumTotalTextBoxNameHere.Visible = False
End if
It's air code and untested, and obviously you need to insert the correct object names as indicated, but it might be worth trying.