Does the orientation of a Bluetooth antenna affect the transmission distance?
Edit: I was wrong, it can. Here's a picture of a similar antenna:



And here's it's radiation pattern:


The radiation pattern is a polar plot of the relative gain of the antenna at each angle. As Andy aka and mouseas pointed out, this plot is in dBi, which is a logarithmic unit (it's dB relative to an ideal isotropic antenna). That means that in some directions, the gain is 10x better than others. Keep in mind that this antenna isn't exactly the same as yours, but it looks like you may see an appreciable difference depending on orientation.