How Would You React When Princess Celestia Approaches You?

[Kurael 43]

I would just make a sligt head nod and talk half formally

[Augman22 1]

I would bow my head while still maintaining eye contact and say Princess Celestia My name is August it’s a pleasure to meet you

[Flew Away 932]

Well, if I see myself in a mirror, I probably shake my mane a bit, and try to look my very best.

[Samurai Equine 52,465]

Let's make one thing absolutely clear...

The greatest princess ever would never approach me. At most, I'd be the one to approach her.
As a samurai who has sworn loyalty to Princess Celestia, if she needed me for anything, she would summon me. Most likely to accomplish an official task. I doubt I am high on her list of contacts since Equestria has its champions, but if ever I can do anything, I am more than willing to serve.  

Secondly, in her presence, I would respectfully bow, admire her greatness, and make haste to fulfill any orders she gives me.  As much I would love a hug, or acknowledgement, or anything more; I dare not ask for it. Would be wrong for a low-ranking samurai to speak out of term. I will only accept what is freely offered to me.