So when I went on a ride the other night and I noticed (rewatching the video my friend took of me) that my inside leg would be constantly bouncing as we were loping around the ring but my outside leg was as steady as could be. We were loping in circles but not tight ones, about the size of half our arena. Just curious if anyone could give me tips on what might help steady my inside leg? Anything helps 
Just a guess of course, but you may be shifting your weight to one side or the other. Most likely your weight is to the outside (centrifugal force) and thus there’s less weight in your inside stirrup. Also possible that you are leaning to the inside of the circle (some of us do this unconsciously) and stiffening the inside leg. Either of these things could make your leg swing.
I suggest you have someone watch you as you circle, looking at your lateral balance from both front and back and help you to find the center.
Or, it could be something else entirely! Good luck.
It’s normal to have some leg swing with the inside leg, the faster you go, the more you swing. However, there can be too much swing. See some leg swing at about 1:13 in this video:
Do you mind posting the video?
I’ll bet the leg swinging isn’t as bad as you think it is. 
Honestly, it’s impossible to have both legs completely still while loping your horse. You have to move! Usually the inside leg is going to move more, if you just think about the motion/direction of the horse’s body. You’ll notice that your inside leg is also slightly more forward than the outside leg.
