There is no prerequisite time. You move on when you feel you are ready to move on. My only suggestion for people before they start looking for other partners is to make sure they are doing it out of a desire for a healthy, balanced relationship, not to stave off loneliness or "fill the void" or get back at your ex. It's important to be able to sit with yourself. I see so many people jump from relationship to relationship because they don't want to be alone and it's just not healthy. So turn inward and ask yourself what your reasons are for getting back out there. If you find the answer is to connect with new people, have enriching life experiences, etc., then by all means, move forward. If it's because you don't want to be alone or you feel that something is missing in your life, maybe take some time to yourself before moving forward.

As for your ex, you aren't responsible for her feelings. It's not up to you to make sure she feels "good" about you moving on. Seeing your partner move on can be difficult, but it's up to us to own our feelings.