After you break up, you do not have any obligations toward your ex. It doesn't matter if you have been together for six months or six years. If it was a bad break up or a mutual breakup. If you loved that person or if you didn't.
The point is, you are not in a relationship with that person anymore and you are not with that person for a reason. You do not owe them time. The choices you make are your own—you don't have to share them. If you want to date, date. If you want to wait, wait. But don't wait for the other person to make their choice first before you act on your own happiness. It's called moving on--and you can't move on if you're still thinking about how the other person feels.
And you know, maybe in moving on, it will help them in doing so too.
Yeah they love you when they need you
But someday you're gonna need to
Find some other kind of place to go.