'She rejected me once, what if she does it again?'

I wanted to marry my girlfriend after dating for three years, so I proposed. She rejected the proposal, saying she needed more time. I was so humiliated and angry that I ended the relationship that same week. This happened six months ago. I miss her terribly, and I know she misses me too, but neither of us wants to make the call and suggest meeting up. I think we could work this out, and I know I acted in a rash manner, but she was inconsiderate, which is what makes it difficult for me to forgive and forget. Also, if we get back together and she decides not to marry me, it will break my heart. I am conflicted about this and don't know how to find a solution.
Letting your ego ruin what may be a special thing is sad. Do you think your girlfriend was justified in asking for more time? I think she was, if you take into account the fact that what you asked her to do was spend the rest of her life with you. Three years is a long time, but both people in a relationship need to arrive at the same stage together, for things to move to the next level. If she is not at the same place you're in, that's perfectly normal and acceptable. If you accept that, you are halfway towards simply calling her and apologising for your outburst. What this boils down to is how important she is in your life, and whether or not her absence will have an adverse impact on your well-being. Think long and hard, then choose wisely.

What is the right amount of time one must stay single after a break-up before moving on to a new relationship?
There is no manual on this. Some people take months, others seemingly move on in minutes. The gap between relationships is not as important as whether or not you actually feel like you want to be with someone new.