Public Displays

I had my first afternoon on my own today.
It was an amazing feeling. It's not really my first afternoon away. It was my first planned one. No kids, just me for about two hours at the library to do what i want: reading or writing.
I chose to write.
This was mostly prompted by learning that Harlequin have read all the competition entries, which means they have read mine! And partly because i really should finish Billie and Cooper's story, titled Agreed: Ten Nights Only, so that they get their HEA. They deserve it and they are still clamouring in my head for that ending. Even though we all know they will get it :)
It was rather strange though. Writing in a public place.
I started at chapter 2 (not going to touch chapter 1 just yet, though i know it needs tweaking but we will waiting for the results of the competition and work on the rest for now) which happens to be quite intense. Cooper is trying to convince Billie to one more night with him, and how does he do this? Confuse her with passion of course ;)
Scenes must arise that of course cause me to hunch slightly over the keyboard and hope those people browsing the shelves for a book to take home to read are not happening to glance at the screen of the laptop and see what i am writing! Mortification.

I know i want to be in the public eye, not me - my writing - but not until it is edited and polished to it's very finest and what i have is the very, very dirty draft.
Being my first foray into the public arena, i felt very exposed and a little preoccupied with those around me and found it a little hard to concentrate on the purpose of my activity. Amazingly i actually got a few words written. I broke the thousand mark which is pleasing.
I wonder if other writers feel self conscious and a bit exposed writing in other places other than their home? Or is that part of the thrill, the drive that keeps and tension, the conflict going in their stories? Or do they just stay in the comfort of their home computer/laptop and create their scenes in peace?