How can I ask a professor I've had as an undergrad for a recommendation
That's certainly fine if you just need a letter resubmitted, but often the best letters are tailored to particular opportunities - i.e., a letter talking about how well-suited user130306 is for Arbitrary Masters Program is going to look funny when you are reading that letter as a committee member for Abroad Research Program.

I would suggest acknowledging in your email that the recommender may need to write a new letter (though the previous one may be suitable as a draft) and ask if they are willing to do so. Implying that they can just resubmit a previous letter might be perceived as (weakly) rude or not understanding what recommendation letters entail.

Also I presume your second letter will come from someone at your current institution? It's certainly okay to use a previous recommender when you have not spent much time at your new institution, but ideally letters come from people who can best describe the current you.