Ardha Baddha Padmottanasana (Half bound lotus) is a one legged balance pose.
Actually, it's a one foot and one hand balance pose. The non-standing leg is in lotus position. The lotus arm grabs the lotus foot from behind the back.
The hand on the standing leg side is on the floor beside the standing foot.
Ashtanga Yoga Poses: Steps for moving into Ardha Baddha Padomttanasana
A pose that simulates ardha baddha padmottanasana, but without the foot in lotus is this quad stretching standing forward bend.
As a substitute for the bound lotus standing forward bend I like this option because the same hand is on the floor and you are holding onto the foot. You can also rotate the thigh outwards so that this pose is even closer to the bound lotus standing forward bend.
Because lotus can be hard on your knee if done unmindfully, I'd suggest one way of learning to do ardha baddha padmottanasana is to practice doing it while laying down on your back. Use a towel around your foot if necessary.
Putting your right foot into lotus hold on the the towel with your left hand. (If you aren't using a towel, hold on to your foot with your hand.)
Pull your heel towards the left side of your lower belly. Try to position the front ankle crease above the center line of your thigh. (Work towards this gradually, let your knee tell you when it is okay to go further.)
Try squeezing your gluteus maximus then releasing it. Focus on a hard squeeze. Hold for two or three breaths and slowly release. See if you hip relaxes as a result.
Note that the purpose of this squeeze isn't to pull your knee down.
If you focus on keeping your knee still, your psoas and illiacus will probably engage to counter the contraction of your butt muscle helping to keep your leg in place.
If you can't squeeze your ass in this position, practice squeezing while standing or in a squat. Find a position where you can cause your ass cheeks to engage. (Pinch a coin between you butt cheeks.) Once you have the feeling then try to duplicate it while doing lotus.
As you relax your glute, see if you can then get your leg deeper into lotus without causing any stress in your knee. Repeat the Butt squeeze two or three times and see if you can gradually work your foot towards lotus.
Try the same thing while standing (without bending over.)
Once you can get the blade of your foot into your hip crease (with center of the blade of your foot over the midline of your thigh) then try bending over and placing both hands on the floor. (Raise the floor by using blocks or a chair if necessary, especially on your first go.)
I would suggest practice slowly bending forwards into Ardha Baddha Padmottanasana and coming up. Get control so that you don't have to worry about falling especially in this position. Also practice sitting down gracefully in case you get dizzy or lose control.
Note, you may get dizzy coming out of ardha baddha padmottansana, particularly after binding.
It may be because blood is allowed to flow in the leg that was in lotus. In either case, be mindful when coming up. If you do feel feint, plant both hands on the floor and make your standing ankle and foot strong. If the dizziness passes, slowly stand up, if it doesn't slowly sit down and rest.
Next to practice grabbing your foot, do the same pose while sitting. With your right foot in lotus, twist your ribcage to the right and grab your foot from behind your back. Once you have a grip, then square yourself to your front and bend forwards.
Note, to grab your foot, if you foot is placed so that you heel is aganst your lower belly and the blade of your foot is in your hip crease, focus on positioning your right shoulder so that it is easy for you to grab your foot. I like to reach my arm forwards, while pulling shoulder blade away from the vertebral column, then I reach my arm to the side and then back. As I reach my arm back, I move my shoulder blade towards my spine. It may help to move it upwards a little as well. From there see if you can grab your foot.
Once you can grab your foot while sitting try it while standing.
While standing, do the forwards bend then try and grab your foot. Once your have your foot you can relax your shoulder. You can work at gradually pulling your foot into your lower belly. Or you can use your foot as an anchor and use your arm to pull your shoulder back.
Once you can bind while bent forwards try binding while standing and then bending forwards.
Note, place your supporting hand beside your supporting foot so that your finger tips are in line with your toes. For balance, separate foot and hand by about a foot.
To come up from ardha baddha padmottanasana, inhale look forwards, hold for an exhale then stand on your next inhale.
To develop more strength and control see how slowly you can stand up.
Release your foot at any point that you need to.