I've been seeing this girl for almost a month now (oneitis, but I'm doing well, multiple dates, sex, time together etc), and I can tell she really likes me, but is not the type of person to just say so outright.

Basically, I wanna get the 'girlfriend/boyfriend' status, but I'm concerning that an alpha male would NEVER initiate such a conversation, and that perhaps it should ALWAYS be left to the girl to bring this situation up.

At first I was too needy with her, and it took me a while to switch into the alpha role, but now I'm here, I'm worried that me initiating such a discussion would be totally the wrong thing to do.

Thanks for any advice, it's most appreciated.

You first need to work on your neediness, after that, a "real" alpha will never be concerned of what people think of him. He does what interests him.
You're interested in start seeing each other exclusively, then go ahead and do it - don't wait for her response, because only chodes overanalyze and overthink everything.

Imagine the worst scenario, you tell her that you want to be exclusive, she laughs her ass at you. Why would you want to be with that type of a girl?

Always remember; Are you having a good time? If your answer is yes, then most likely you're on the right way.

If you're looking for a way to do it - me and my current girlfriend met through Facebook.
She brought up the relationship thing in a very fine way - she simply asked me - "so...do you want to change our relationship status?" - and I indeed was interested - so I agreed.

you have to show that you're vulnerable eventually lol.. you cant just be this hard arse bloke that has no feelings and shows no emotion lol.. ask her mate... an alpha knows and gets what he wants remember that... hope that helped