Do it! I do it all the time, I have my regular places now and the bartenders know me. I know some regular patrons too now.
I also like going to bars early in the evenings on weekends before it gets crowded, it's still quiet then.
If I'm not in a talkative mood, I have my book or tablet with me.
Go a few times and you'll get comfortable talking to people. Make friends with the bartender. Look over at your neighbors, say hi, ask them how it's going. I go to places that serve cool beer and drinks, so I'll ask what they're drinking, what kind of beers do they like, etc. I meet tons of people, usually just a nice conversation. I don't need a date from every conversation, I just enjoy talking to people - unless I'm in a mood lol.
Going out a big sports night is a good idea too. Even if you don't care about the game, there's lots of men there.
Go with a friend if you're nervous. Just one friend, maybe too. Don't go with a gang of women.
If you're in DC, let me know. I'll be your wingwoman
ETA: If your goal is to meet people, I agree with not being engrossed with your phone. If I have my tablet, it's usually because I'm doing a crossword or reading an e-book. But reading a regular book looks friendlier to me and it's a conversation starter (what are you reading?).
