While it is not currently possible to remove the scroll bars, it IS possible to mostly hide them with CSS.
.your-selector *.column-header-background *.show-hide-columns-button,
.your-selector *.scroll-bar:vertical *.increment-button,
.your-selector *.scroll-bar:vertical *.decrement-button,
.your-selector *.scroll-bar:vertical *.increment-arrow,
.your-selector *.scroll-bar:vertical *.decrement-arrow {
-fx-background-color: null;
-fx-background-radius: 0;
-fx-background-insets: 0;
-fx-padding: 0;
-fx-shape: null;
}
.your-selector *.scroll-bar:horizontal,
.your-selector *.scroll-bar:horizontal *.track,
.your-selector *.scroll-bar:horizontal *.track-background,
.your-selector *.scroll-bar:horizontal *.thumb,
.your-selector *.scroll-bar:horizontal *.increment-button,
.your-selector *.scroll-bar:horizontal *.decrement-button,
.your-selector *.scroll-bar:horizontal *.increment-arrow,
.your-selector *.scroll-bar:horizontal *.decrement-arrow {
-fx-base: transparent;
-fx-background-color: white;
}