I'm not sure if this is the right way to do it, but I've achieved this effect in the past by adding a theme to the
ScrollContainer, or any GUI node above it in the hierarchy.
Edit the theme, and choose "Add Class Items" from the "Edit Theme" button, choose
VScrollBar. Then in the settings for those types, set the various styles to
NewStyleBoxEmpty. The scrollbar will no longer be drawn. I've put together a simple example of hiding just the HScrollbar, here.