You and your horse are just lovely, you definitely look tense and a little too far forward, maybe anticipation?
At the beginning of every ride I do a few things:
-Stand up out of the saddle, straight up, not half seat, and walk around. I guarantee you'll spend 2-10 minutes just trying to find your center and not fall back into the saddle. I don't care what line your legs are in, every human is going to be a little different, what matters is where YOUR center of balance is. This will force you to be balanced. If you fall forward your legs are too far back, fall back legs are too far forward, find your center. :) I do this EVERY ride to just find out how balanced I really am today.
-Spend the next few minutes walking with my legs perched over the knee rolls of my saddle, so I'm sitting VERY chair position. You need a good horse to do this with ;) but it helps push you onto the back of your bum and sit more properly in your seat, for people like me and you who get a little too ahead of ourselves.
-sitting normally again, balanced and relaxed, moving my legs and hips with the horse, I make circles with my shoulders. This will also help with the too-far-forward problem, make the circles backwards, so your rolling your shoulders up and toward your back, down and toward your front. This will open up your chest and allow for more proper breathing.
-Focus on breathing deep down into your belly button, nervous people like us tend to breath shallow, into our chest, breathing down into your belly and letting it out slow helps get oxygen all the way in and release all the toxins. This will also generally help relax you :) Remember to do this all throughout your ride.
-whenever I feel myself feeling a little off balance I go back to my standing straight up exercise. Find you center again, then go back to your mission.
-I ride at least 50% bareback, clearly those exercises aren't easy bareback, so don't worry about them. But bareback is a great way to build up core muscles and learn to feel your horse. Just practice a lot of walk/trot transitions bareback. In order to have comfortable transitions bareback you NEED to be balanced, this will help you feel any little areas you aren't balanced in. Practice lots of circles, serpentines, zig-zags, ground poles in your half seat. Riding round the ring over and over is boring and taxing for your horse, but it's also not helping you any. If you have 30-60 minutes to ride, make the most of it, build your muscles and core strength by doing lots of work while riding.
Walk/trot is the best work for building strength and balance (for the rider) but do stuff while you're doing it, remember to use your WHOLE body for every request, use your seat and legs for steering more than your hands.
You are looking great, your horse looks like a doll <3 Post more pics soon!