You want to absolutely minimize the chance of rejection? Never talk to a girl, never ask a girl for a date, never be unfaithful to your right hand, never take a chance.
Don't worry about the chance of rejection. You never know whether she might say yes and if you assume otherwise, you could be bypassing an excellent opportunity. Allow yourself to become inured to rejection and you will develop self-confidence. (I know it sounds paradoxical but it is true.)
There is always a risk. Saying that you want to minimize it is another way of saying your not in it. And it's not attractive to anybody, male or female. Your saying your not willing to take chances. And that you'll back down when theirs always a problem, because your unwilling to fix it. No offense. But that's the truth. Relationships are about pursuits. And there are plenty of people who are shy, but are able to get a relationship. Your just making it an excuse. I'm sorry, but unless she does the asking, your left to figuring it out.