Why? What's the point?
Whether you're looking up or down isn't the point. I can have my head facing down and my heart facing any direction at all. I think we make this mistake a lot (I know I do). We do the "right thing" on the outside, when the inside is all that matters.
I can have my head facing any direction I want when I pray, but if my heart is not in the right place it's all just for show.
Yes, this post is about praying, but this idea transcends prayer. Don't focus on looking the part. Don't focus on whether or not the people around you think you're doing the right thing. Do the right thing.
Whether you'll do it or not depends on whether or not you want short-term recognition or long-term change. So, which are you aiming for?
[Speaking of bowing your head to pray, what do you think of this?]