I want to apply for master’s programs, but I need two letters of recommendation. I was never very close with any of my professors, though I did receive good grades in all of my classes. The professor who probably knows me the best is one of the core faculty at the college. I asked her for advice on how to start with undergraduate research, which wasn’t a requirement, just an interest of mine. I also received an A in her class, and suggested an outing for the class which she then took up. It’s also been about a year since I graduated. Would it be appropriate to ask her if she could write a letter of recommendation, perhaps in exchange for some gofer work (filing, watching class while students take tests, running errands)?
It’s appropriate to ask for a letter, but completely inappropriate to offer a thing of value in exchange. Professors are already paid to do their job, which includes writing letters of recommendation, and it would be unethical for a professor to accept a favor or other thing of value in exchange for agreeing to do what is already a part of their job.
Just ask for the letter. Writing recommendation letters is part of a professor's job. No need to be a gofer, and importantly, offering some sort of service in exchange for a recommendation sets up an unethical situation: recommendation letters should not be paid for in any way.
Assuming your request is granted, it might be helpful to remind her of some of the things you've done related to her course, etc, as you've included here, since professors have many students and may not recall all the details.
A much better way to help out this professor is simply to remind them about your interactions ("I took class X and received an A and you gave me excellent advice on how to start my undergraduate research project") so that it's easier for her to recall your background and actually write the letter.
I remember being mildly upset by the fact that I had a letter of rec written by a professor who remembered me by name, yet several years later the letter was accidently given to me, I saw they had written "He received an A in Linear Algebra from me", when it should have been Differential Equations.