we still maintain a casual friendship,
That's your problem right there. You have some residual feelings for this girl and therefore, being in a relationship you should NOT be maintaining any kind of so called 'friendship' of any kind with her. You're crossing a very fundamental relationship boundary on your new girlfriend. Your ex is with someone new. You are with someone new. Do everyone a favour and stop talking to one another all together so that you can put the past in the past and leave it there where it belongs.
I don't know about anyone else in the forum but I'm getting really exasperated with reading about all these young people who keep past lovers in their lives as "friends." You CAN NOT be friends with someone who you have feelings for and keep it drama free and platonic. It's IMPOSSIBLE 99.9% of the time.
Move on, do the mental work to put this away for good and concentrate on the lovely girl you've got in front of you instead of looking in the rear view mirror and wonder what if. Life travels is in drive, not reverse.
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion