She says no to physical intimacy

Is it normal for two people who are engaged to avoid getting too physically intimate? My fiance and I have been dating for a little over a year and don’t really get too close because she is quite prudish and feels as if we should wait until marriage. I am okay with waiting, but I also worry about how compatible we may be because there is no way for me to find out. I don’t want to make it sound as if sex is the most important part of our relationship, but it is not something I can ignore either given that this is someone I intend to spend the rest of my life with. My fiance is more optimistic about this than I am, and believes I should stop worrying about it. I want to, but can’t seem to let go of the idea. How do I cope with this situation without letting my fiance worry about it?
You’re right about the importance of physical intimacy, but you can’t force your fiance to do anything she isn’t comfortable with either. It’s great that she trusts you will both be happy on this front, and you may simply have to take that leap of faith with her. It is also a very positive sign that you can both discuss these fears, because brushing them aside and hoping things will work out isn’t a solution. I suggest you keep talking about it, give her a sense of why this troubles you, and focus on building trust and a stronger mental connection. If you are both committed to making this work, and love each other enough to trust each other with your expectations, the physical aspect of your relationship will only evolve and get better with time.

Should I ask someone out after just one meeting? Does that make me seem desperate?
That depends upon the nature of the meeting and what cues you have picked up. You can always be direct and ask, provided you are prepared for rejection.