Should I ask a reference letter from someone working where I am applying to use it for another application?
I understand your hesitation and there may be situations in which your concerns are spot on. That said, people in the position of researcher A exist to support and further the successful outcomes of their students. Outside specific research contributions, this is their legacy. One of the most rewarding aspects of leadership is helping people succeed. 

Based on your question, I recommend immediately asking researcher A for a recommendation letter. Discuss any concerns with them directly and save yourself the worrying. You can always draft the letter for them and let them make revisions as they see fit. 

Good luck!