Remember that your LBS is used to working with new or returning riders so they've likely seen it all. If I remember correctly, I took a fall the first time I test rode my road bike. I can't even remember what boneheaded thing I did that made me fall. I laughed, dusted myself off and moved on. Thankfully, the fall hasn't been indicative of my skills as as cyclist.
I understand your fear of embarrassing yourself, but you'll end up being a lot more embarrassed if you buy a bike that doesn't fit or handle well. Learning to laugh at yourself is a good skill to have. Every cyclist I know has fallen or done something stupid/silly/embarrassing on their bike. Just do a search for clipless pedals and you'll read about a fair number of falls; it's a right of passage. The sooner you get over self-consciousness, the better.
Admittedly, relearning to ride a bike as an adult isn't brain surgery, but it also isn't as easy or intuitive as it was when we were kids. There are things you have to learn how to do and do safely and skillfully on a bike that take some courage. Treat test riding the bikes in the parking lot as good practice for what's to come. I'd further encourage you to embrace such acts of courage. They're what lead to a sense of accomplishment and victory.
Good luck.
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher