Oh yes, there are many other expressions that people use when they are parting.
For example, if they have a plan to see you soon, tomorrow, next week etc., they might say:
: "Talk to you later," or "Until tomorrow."
If there's no plan to see you soon, and they want to get together again, they might say: "Don't be a stranger," or "Let's stay in touch."
There are a lot more ways that people say "goodbye." You could probably find more if you spend some time listening to TV shows; just focus on how the different characters say goodbye in different contexts. I bet that would be a fun research project!