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I've been waitlisted at BU, and really want to get in.

I don't know how to approach asking for an additional LoR from a professor I had last semester. She was a great prof, knew me well, has an incredibly accomplished background. However she's extremely busy, and doesn't hold regular office hours anymore. I asked for my original LoRs in person, but I don't know if it's possible for me to do that with this recommender. Should I go ahead and send her an email requesting a rec letter, or should I call her office and try and book an appointment?

I'd send an email, I'd just allude to the fact that you're sending over email because you weren't sure when a good time to come by the office was. Make the request brief and then offer to come discuss it in person at a time that's convenient for them. That's basically what I did because I asked for a letter a year after I graduated. I'd write something like:

"Dear [Professor],

I hope you're doing well! As you know, I'm planning to attend law school next year and I've currently been waitlisted at one of my top choices. I have the opportunity to submit additional letters of recommendation and was wondering if you might be willing to write one. I would have preferred to ask this in person but I was unsure of your office hours and didn't want to delay. If you're open to it, I'd be more than happy to discuss it in person or provide you with any more information that might be helpful!

Sincerely,

[You}"