Most faculty that have interaction with medical students are accustomed to people asking for letters, they had to do it at one point as well. Work hard during your week, get to know the person, and then ask for a letter. What is the big deal? I must reiterate that you qualify your statement by saying STRONG letter. You can take it or leave it. They can write it and if you later feel that you have a better letter just don't submit the one from said letter writer... So, if you are not aware yet, your school uploads all of your LORs to ERAS and then you choose which to send to each program. So get a letter from you PD as well. Sometimes letter writers let you see the letter too.
Don't be scared to ask for a letter, it will not hurt you, unless you acted like a jacka$$ for the week.
I received one from our chair of internal medicine after working with him for about 1.5 weeks and really didn't get much time with him because it was a big team and he was always leaving for administrative duties. It ended up being an excellent letter and was mentioned multiple times.
Time isn't necessarily a problem, base it off of your perception of the interaction, if it went well then try and get a letter.