You are totally asking the wrong person here! I could ask my mom, she did some dressage and knows how to sidepass but her horse is actually trained for it. My mare just looks at me like i"m nuts. This is some of what I've been told though:
My understanding is you "close" their options by keeping even pressure on both reins, take ALL pressure off from the leg you want them to move towards, and apply firm, steady pressure at the girth with the leg you want them to move away from. (in front of the girth turns the front end, back of the girth turns the back end, ON the girth is for sidepassing). So maybe your leg/girth position is causing you trouble, if she thinks pressure on the girth means turn the front end (spin). Now, if you are bareback, obviously you'll have to pretend a girth is there, hehe. So you'll have to work out a specific location for each movement.
What are you using for a bridle? When going bitless I tend to use a sidepull or indian hackmore, I have something of an issue with rope halters not being very "clear" to the horse at times. Even a regular halter with reins clipped on gives both you and the horse something simple to understand. The reason I ask, everyone always says that about "closing" their forward options by even pressure on the reins, kind of hard to do with a rope halter and a single lead rope.
I've been told to start off doing half passes first (forward and sideways on a diagonal direction, instead of sideways with no forward movement), as those are physically easier and the horse gets a better idea of what you are asking for, and when working on side passes, to face the horse against the wall so they can't go forward but only side to side (or spin, or back, whoops! LOL).
To give yourself and the horse something to focus on and maybe make it a bit easier, try to sidepass down the length of a ground pole (or 2x4 or PVC pipe) instead of just trying to do it in the middle of an open area. Sometimes if you aren't focusing on your body, but more on a target, you allow yourself to give the horse the commands they need to understand what you want, if that makes sense.
One thing that a lot of "trainers" frown upon but I swear by.. vocal commands! You said your mare knows how to sidepass from the ground, start using the vocal command along with the pressure on the ground and praise the heck out of her. I use "side". Then, from the saddle, using the same command along with the leg pressure, she might be able to make the connection easier. This works better with some horses than others, but nearly every horse learns faster if they can link their "new" lesson to something they already know. I've been trying to establish this command with my 4 year old (I'm not riding him yet, he's way behind development wise) but he doesn't quite get that I want him to move his entire body, and his feet get tangled

. They do get confused sometimes, and you just have to be patient.
And the biggest thing of all, if you are having a bad time and just CAN'T get it, stop and ask the horse to do something simple and easy that you know they can do well, and praise them up when they do it. That way neither of you feels like it was just a huge arguing session and walk away mad at each other, and often, the horse will think about it in the mean time and next time, do much better. If they just get turned out knowing you are mad and they don't know why, they'll just figure you're nuts and not worry about it
If nothing else, that gives you some stuff to try. Hope you have an indoor, its been dang cold riding lately!