The phrase you're looking for is "bubble nucleation." Bubbles don't really just form spontaneously. They need something to start the process, after which they grow larger until they are big enough to float upward. If there's a single place where they seem to form more consistently, it's because there is something different about that spot. Most likely, there's a small irregularity in the glass there... probably a small bump. That irregularity makes it easy for bubbles to form.

In a similar vein, when you're doing lab chemistry, there are many chemicals you want to boil in the most controlled way possible because they're dangerous if they get out of control. One way to do that is to deliberately introduce something into the beaker that will allow the bubbles to form smaller, faster, and more easily. "Boiling chips" are added to accompany this. They are small pieces of an inert substance that have lots of edges and points (much like the glass irregularities in the champagne bottle or cup that you observed.)

Here is a YouTube video that shows some boiling chips in action.