Bubble wrap is recyclable in plastic bag drop-off stations. You don’t have to pop the bubbles.
See https://how2recycle.info/sdo for more plastic bag and plastic film acceptable items and recycling locations. Most grocery stores have bag recycling stations located near the store entrance, sometimes the exit, where you can put bags and film in.
If you live in Austin, you can drop bubble wrap and other clean and dry plastic bags and film off at the Recycle & Reuse Drop-off Center at the Plastic Bags recycling station next to the Cardboard station. RRDC is only open by appointments right now so be sure to sign up first.
This bubble wrap is from glass supplement bottles. Regardless of manufacturer it seems like most companies ship glass bottle supplements wrapped in bubble wrap so keep that in mind when placing orders.