"Have you seen Julie recently?" implies that you have known her for quite some time.
"I met her a few days ago" implies that you had never encountered (met) her until that exact moment.
I don't agree. Meeting someone can be a recurring event.
We meet every Thursday morning.
We have met almost every Thursday for the last seven years.
("meet")("met") and ("see")("saw") can have different meanings; meeting someone is more involved than justseeing them.
So the only form of B. that makes sense is,
"Yes, I saw her a few days ago.". I don't agree.
Have you seen Julie recently?
Yes, I met her a few days ago. (I didn't just see her; I met her.)