Poly mailers and Kraft envelopes are both recyclable. Bubble mailers on the other hand (also known as bubble padded envelopes) they are also recyclable, however, bubble must be separated from the envelope by the consumer, that's because most recyclers don't have such capabilities because of high labor costs. Remember, recycling has to be profitable in order to make it work.
What can you do to make recycling work? Wrap fragile items in bubble wrap first and put it in envelope using Poly or Kraft envelope, all these materials are recyclable as long as they are not attached (laminated) to one another