When im around friends, im a natural alpha male.
When im around females im not interested in, I become a natural alpha male.
Why is it that when I am alone in public, or when im around a female i have an interest in, I suddenly become a beta? Is there any way I can fix this annoying problem?

I strongly believe that this common issue is a matter of Inner Game.

It's because it all starts with your beliefs, how you interpret reality, etc.

You see, when it comes to the topic of women you're interested in hooking up with, you have a web of beliefs that say the following kinds of things:
1. Hooking up with her means getting something from her
2. I need to impress her in order to earn hooking up with her
3. I might not be good enough to earn that right
...etc.

It's very much how most people new to the job market see job interviews. They, for some reason, feel inherently unqualified for the position they're applying for simply from the fact that they did not have that job before. They feel like they're taking something from the company (money) if they land the job. They feel the need to impress the interviewer. They doubt their own qualifications since they don't know what it's going to be like to work there.

In the first month of my Seductive Introvert program, I help you fix all of these Inner Game issues so that your brain will be finely-tuned and prepared for pickup, but I'll tell you what you need to believe to solve your current problem right here right now.

First of all, you need to recognize that hooking up with a woman you're attracted to is by no means "getting" something from her. You have a lot to offer to rock a girl's world and you know it (if not, you should!). Same goes with a job interview. The company you're applying to work at needs a hole in their company filled. And you can fill that hole. We could go deeper here with techniques of how you can solidify your confidence of really knowing that you have a lot to offer to girls you're attracted to, but let's move on.

Second, now that you know that hooking up with a girl does NOT equal getting something from her, there's nothing to earn! You've already "earned" whatever qualifications by being your awesome self. Pickup and seduction isn't about impressing women, anyway. It's about connecting with them. So start finding out more about HER to see if you can find some common ground instead of worrying about proving yourself to her.

...and from there on out it's all a matter of Outer Game.

Chief said it all, but I'd like to address some problems you might seem to have too.

Immediately abandon any rating scale you are using, as that affects how you perceive women and you start becoming more needy; thus, lowering your chances of success and making you more anxious when you speak to girls. Remember that you need to get HER talking to you instead of the other way around.

Consider it as meeting a new friend. Get to know her life, background, hobbies, interests and passions. I am sure by the time she talks about one of those topics, some interesting topic will pop up. Try to build inside jokes too, they are a great way of connecting two people together and getting rid of that extra insecurity people have for strangers.

Having said all that, think of the girl you are interested in as a normal human being. You are both the same. Do not under any circumstance differentiate her from any other girl you talked to.