What is the etiquette for making an appointment to request a letter of recommendation? I'm currently a college sophomore looking to transfer to a university overseas, and I need a letter of recommendation from my adviser in order to apply. 

Usually, in order to get in touch with my adviser, I just sign up for a 20 minute time slot, but that system is usually intended for students to quickly discuss class options. 

I feel like signing up for the time slot and asking her for a letter of recommendation in person with no warning is sort of rude, and I've also heard that asking for a letter entirely over email is also rude. So, scheduling an appointment over email seems like the best option, but I'm not sure if I should explicitly reference my transferring and the letter of recommendation, because that seems tantamount to just asking over email. Any suggestions?
The reason to want to talk in person is to be able to have the space for discussion and nuance that may be impossible over email.  But you can certainly start the discussion over email.  Why not send an email saying your plans and that you are interested in getting a letter of recommendation, but then close by saying that if the professor is willing, you think it might be a good idea to meet to discuss?