Billy Joel - The Pianoman.
The better choice is to watch the movie at home. Then you can pause it when you need to use the bathroom, you can eat whatever food/snacks you want without paying a fortune, the sound won't be too loud, you won't have to deal with obnoxious jerks around you, you won't have to worry about getting shot by some crazy off-duty cop, you won't have to sit through 30 minutes of ads, I could go on and on...
Its easier to get fully immersed. Its easier to find a seat. I can still chat with friends who saw the movie later by themselves.
You enjoy sitting there uncomfortable with a full bladder? Or you don't mind missing 5 minutes of the movie when you need to go?
It's ok to go to movies with other people too, but you aren't really socializing while you are watching the movie, unless you want to disturb the people around you.
However, I do want to take away the stigma of eating alone, watching a movie alone, etc. In my previous life, I was a tech consultant who traveled with a team and then was left behind by myself to finish the job. I spent more time alone in New Orleans, Columbus, Newark, and Dallas than I would have ever expected.
What I learned is that many people are alone. Those of us that were alone, together often met others and weren't so alone. It made the time better.
More importantly, you may not want to go out and eat dinner or go to a movie. That is a reasonable choice. That said, if you do and if you are worried about people thinking about you being alone you should know that most people don't notice anyone else. So they are not making judgments.
Most importantly, there are a lot of us who are alone out there. If you sit at the bar (and don't worry about drinking or not), you'll fit right in with the rest of us who are doing the same thing. We're all in this together.