I am currently doing an unpaid internship that I am receiving college credit for this semester. I really enjoy working with my manager and after reading your previous post on extending the length of an internship, I decided to ask my manager about it. She was fine with it when I asked; however, she is always so busy between meetings, dealing with employees and doing her own work that I am often left just sitting there in her office watching her or I am asked to leave when she has an important meeting with someone. It's an internship where I am given random stuff to do so I do not have an actual desk/computer or any routine work that I can do when I come in. I tried talking to her about it a bit, but she only admited that her work keeps her busy.
What I like about it is that I can receive credit for a class and also, she really does try to do her best to make time for me when she can, but I feel like I am in her way or bothering her in her work at times. Is this worth extending the internship?
Well, first, I don't think you should make your decision based on a worry that you're in your manager's way. If you are, that's her issue to deal with -- by not saying yes to the extension. You're better off just having faith that she'll tell you if she can't accommodate the internship anymore, since otherwise you risk driving yourself crazy worrying that you're secretly burdening her.
Now, as for whether or not to extend the internship: It depends on what you want to get out of it. If you feel like you're learning things and getting useful experience, then sure. But otherwise, I would move on and look at other interning or volunteer opportunities that will benefit you in ways that this one isn't. I can't actually tell from your letter whether you feel like you're getting much out of this one or not; much of what you wrote sounds like it's not the most fruitful experience for you, but you do say that you're enjoying it, and I can't tell if you're bored or not, so a lot depends on that.
However, if you do want to stay, look for ways to improve the experience. Do you see projects that might be useful for you to take on? Or can you talk to her about whether there's something that you might work on long-term so that she doesn't need to spend time coming up with ways to occupy you? The best project in this situation would be something that would (a) benefit the company in some way, (b) not require tons of guidance from her, (c) take a good chunk of your time, and (d) not be high-risk, meaning that if it doesn't go perfectly, nothing disastrous will happen (so that she won't feel the only way you could do it is with a lot of guidance or oversight from her).
But you can also always look at other internships out there. You might end up in something you like better, so I'd take a look at what other options you have as well. Good luck!