Yes, it's allowed. Unless the bouncer realizes how clumsy you are, then they might have something to say.

I've done it. I've taken a book, I've not taken a book. I've wall-flowered and people-watched, I've introduced myself. If you liked sports I'd tell you to go to a sporty bar on football day. People can't help talking to each other in a place like that.

It can be unnerving, but that's mostly all in your head. Everyone else in a bar is busy doing his/her own thing. They are very unlikely to care what you're doing there if you're not putting yourself in the middle of things. If you are putting yourself out there, it's not usually very difficult for a first timer to get a conversation going- what type of drinks you should try, what bars around are good places, etc. Start with the bartender if you're too freaked out. Tip well.