Scofield,
Its actually a big step to even go out on your own, I was too intimidated to do it for the longest time, and many of my friends who get all sorts of girls would never even think of entering a bar or club alone, but it is very liberating and allows you to focus on improving your game without the social risk involved with so-called 'public' failure.
What I have found is the most important thing about going out alone is confidence. There is no reason to fear rejection going out alone; most if not all girls spoken to will be strangers, no one is there to judge you, and it is much easier to play the part of the mysterious lover when you are by yourself.
I have found that even in relatively small bars, it is hard to be pointed out and called out as being alone and be judged for it. Most of this you will encounter will be a small mention of "So where are your friends tonight?" or "Are you here with anybody?" which can be easily brushed off with an offhand comment about how they were moping around and didn't want to go out, or an expression of your desire to meet new people and expand your horizons.
Logistics also tend to be much more flexible when you are alone because you (rather than the people you came with if they brought you) decide when you are leaving and where you will go. Always make sure that you do have a way to get to a place you can get intimate with a girl in when you go out alone; I have been out alone and brought a girl to where she was begging to get somewhere to have sex with me, then all of a sudden realized that all I have to get back to my dwelling is my own two feet. If you live close to the bars and clubs this is easy, but if you don't it can be an almost comically frustrating situation (assuming cab fare is as ridiculous in your area as it is for an unemployed college student in mine).
As to the volume of girls problem, that one is easily solved; switch bars or clubs! There should typically be other bars around the one you are at to move to if you don't like the crowd in a certain one, and clubs are in my experience very rarely not within easy walking distance of many other clubs. This can also be an easy way to escape a conversation gone awry where the place is too small for you to non-awkwardly switch to gaming another girl without the previous interaction being witnessed by said girl.
There is also an easy solution to being in a loud club where everyone is dancing and you can't dance...DANCE. Even if you absolutely and unequivocally suck donkey dick at dancing, the only way to get better is to try it, and it isn't as hard as you think. Club dancing in this day and age typically only involves a basic sense of rhythm and remembering to move your feet and hips. However dance floor pickup is not particularly beginner friendly, because it involves implementing pretty advanced physical game and leads to difficulties in maintaining attraction long enough to move a girl all the way back to your place that require rapid connection building, confident power, and mastery of sexual tension to ameliorate. That being said dance floor game is good for beginners to practice at dancing, learning touch, and nonverbally creating sexual tension; but tends not to be a great place to focus on for trying to close in the early stages of building your game. Your best bet is to stick to bars and the bar area of clubs, that area will lead to a lot more success early on.