It means he understood that you had said 'goodbye' and was honoring your wish to end the relationship. When you end a relationship, it ENDS. Someone gets the last word, and in this case it was you. If he replied to you, then you might have replied to him, and who knows when the END would have happened.

When a man says bye for now?

“Bye for now” is an overly friendly way of saying “bye”. It's just for when you want to put emphasis on seeing the person again. It's good for any situation that isn't professional.

How do you respond to a bye?

See you later, later, see ya, bye, bye-bye, catch you later... use whatever you want. There's no "better" one. The best one is the one you feel like saying.