You can use overflow-x: hidden; overflow-y: scroll (or auto instead of scroll).
x is the horizontal scrollbar, y is the vertical.
Play with these options until you get what you want.
You say if they have a small monitor the horizontal scroll bar comes up but if your image is a background image it should not create a scrollbar on its own; there must be something wide inside a div or table cell to cause a horizontal scrollbar.
Code downloaded to my PC will be deleted in due course.
WIN7; IE9, Firefox, Opera, Chrome and Safari for Windows; screen resolution usually 1366*768.
Also IE6 on W98 with 800*600 and IE8 on Vista 1440*900.