I only wear them with leggings or skinny jeans when I go over to a relative's house and somewhat 'proper' attire is required. Honestly though, I prefer the comfort of traditional bottoms over jeans :p
It took me a realllly long time to wrap my head around the idea of 'fusion' fashion...I really didn't like mixing East and West and wearing kurtas over jeans in public. I love wearing Indian clothes, and I love my American clothes, and while I have friends who can and do wear the mixed look with lots of style, I felt like it drew too much attention to me. Its still not something that I wear as part of my usual wardrobe... I have a friend who designs fusion clothing and I've worn some of her styles to work and gotten lots of compliments, but I never feel like I'm in my own skin when I do that.
As for your kurta...its beautiful and I wish I could see more detail...I think its long enough to be a dress actually. Add a long pendant necklace or a scarf, or a belt and you've got a full outfit