Your helmet looks really small o.O haha,
As for your posture it's really hard to have a 'correct' posture/position bareback, it really depends on how the horse is built. Yes ideally your legs should be a touch back which comes naturally in a saddle and for you to roll your bum under (sit on your pockets) but keeping a nice straight back(like you have)
You don't look at all big for that horse, STB? He seems to be built down hill which is why you would have to tendency to lean a little back and put your legs forward.
Don't be to harsh on yourself while bareback, your position at the halt and walk are great. But keep riding bareback! Great for your balance, and being able to feel the horse more. (: