Have you looked into ControlsFx Popover control.
import org.controlsfx.control.PopOver;
import org.controlsfx.control.PopOver.ArrowLocation;
private PopOver item;
final Scene scene = addItemButton.getScene();
final Point2D windowCoord = new Point2D(scene.getWindow()
.getX(), scene.getWindow().getY());
final Point2D sceneCoord = new Point2D(scene.getX(), scene.
getY());
final Point2D nodeCoord = addItemButton.localToScene(0.0,
0.0);
final double clickX = Math.round(windowCoord.getX()
+ sceneCoord.getY() + nodeCoord.getX());
final double clickY = Math.round(windowCoord.getY()
+ sceneCoord.getY() + nodeCoord.getY());
item.setContentNode(addItemScreen);
item.setArrowLocation(ArrowLocation.BOTTOM_LEFT);
item.setCornerRadius(4);
item.setDetachedTitle("Add New Item");
item.show(addItemButton.getParent(), clickX, clickY);
This is only an example but a PopOver sounds like it could accomplish what you want. Check out the documentation for more info.
Important note: ControlsFX will only work on JavaFX 8.0 b118 or later.