It's perfectly normal to feel nervous as you approach a girl, or as you plan to approach a girl. Especially in your early stages of practice; you're just not used to it yet.
So, get used to it! Get used to that feeling. It will not go away just yet. What you need to do is push through it. All of us may feel nervous; we are human, you know. Girls get nervous when a hot guy approaches them--they react in various ways...some are rude, and cold, whereas others are warm, and energetic.
Approach that girl, with that uneasy feeling in your stomach as you exit your comfort zone, and be bold. Say Hey as if today's the last day you will live.
And I can guarantee you, after the approach, and possibly the introduction, you will not feel scared, or nervous! Then, you will walk away from the girl thinking, "Oh man Fitch was absolutely correct! There is nothing wrong with feeling nervous, but what the hell was I nervous for; it was nothing!"
Ignore your brain, as it tries to second guess your actions. It never helps anyone. It resulted in Hamlet's downfall, Oedipus's downfall, and people in our generation. Over-thinking is hazardous. You resolved to approach this particular girl, NOW do it--with that uncomfortable feeling in your stomach that you will soon miss as you reflect back on your younger days.