Do the same things at the same time. This will make the distance between you seem smaller and more bridgeable. You'll feel closer together and you'll be bonding at the same time.
Cook the same meal or menu every so often. Even if you don't both cook, you could both enjoy fresh fruit in season or choose a common snack.
Read the same book or article. You can even take turns reading it aloud to each other.
Watch a TV show or movie simultaneously. Keep a call open and share your reactions.