It's totally fine to go alone. Your experience going alone could vary wildly, though. I have gone to bars alone and had great conversations with the bartender and had him introduce me to other people he thinks I'd like talking to, etc. I've also gone and been completely ignored by pretty much everyone because they were there with their own friends doing their own thing.

Mentally prepare for feelings of self-consciousness or feeling out of place and let them pass. We all feel that way sometimes and those feelings are not a reflection of the truth. You have every right to be there.

Also, never put down your drink and pick it back up. Someone could put something in it. It's not likely and I'm not trying to scare you, it's just part of "Bar Alone 101".