There are a number of Yoga asanas that can worsen bulged discs. Let me look into them, but a number are common asanas, you could probably research them also. There are some that are helpful.
I looked at the youtube video. Bear in mind that is common sciatica they are dealing with. A bulged disc puts you in a new category. If you want to do Dhanurasana I would suggest only reaching for your legs but not arching your back. Make sure you only feel it in your legs.
I just spent the last weekend doing the module on back bends and we discussed slipped discs quite a bit.
I would also suggest child’s pose, and all of it’s variations.
I would avoid Cobra/Bhujangasana, and Wheel/UrdhvaDhanurasana, Virabhandrasana 2/Warrior 2, Viraparita Virabhadrasana/Reverse Warrior, Revolved Triangle/Parivritta Trikonasana, Uttanasana/Forward Fold, Lung Twist, Thread the Needle, and actually most twists will be an issue. Take it easy, and be careful.
Here is a good one to do Wide Leg Standing Forward Fold/Prasarita Padottanasana. You might want to use blocks, and try to remember Tadasana when you are working through it. Reach forward with your head. Also, legs up the wall with a bolster under your butt, and lower back. That is a low stress way to relieve pain, and stretch with little effort.
I’d say look around for more info on helpful poses that do not stress the lower back. Look for information about the bulging discs and not sciatica.