I THINK I FIGURED OUT THE BRAND OF THE BAG!! yay!!!
I am pretty sure it is Temperley London. If you go their website, the logo looks incredibly similiar and it is written in script too (which makes it hard to read).
they don't show their bags specifically on their website so now i am going to google until i make sure it is temperley. i didn't know they made bags! and Blair is going to wear a temperley dress in an upcoming episode, so it would make sense to be a temperely bag because usually designers lend a bunch of stuff at once to the show..
i am so proud right now...lol