For molecules to be enantiomers, do their bonds have to point the same way?
Place your two hands face down on a table. They are non-superimposable mirror images of one another (chirality does come from the Greek kheir, meaning "hand", after all). Now flip one of your hands over so that one palm is facing up. Are your hands any different now than before you flipped one over?

No. Your hands' orientations in space have no effect on their superimposability, as is the same for molecules.