Here's the deal: The Post Office clerks see a bubble envelope and automatically classify it as a "package" and charge you the "package" rate ($6.55 and up). It's NOT because it doesn't bend (rigid) - that simply means it is "non-machinable" and subject to a 21-cent surcharge.
If you look at the Domestic Mail Manual (DMM), you will see that there is a discrepancy between classifications of "letter", "large envelope" and "package" (I think those are the terms) and what happens when those items are between the magic thickness dimensions of .25" to .75". If you look in one place, it seems to say anything above .25" thick is a package, regardless of the other dimensions (length and width). Elsewhere in the DMM, if a "large envelope" - which is an envelope with L and/or W between certain ranges - is between .25" and .75" thick, then it has it's own rate (slightly higher than letter but far below package). Back when the postage increases were first implemented in Feb, 2013, I was successful at sending my #000 mailers at the large envelope rate by using the Automated Postal Machine kiosk thingy and avoiding the clerks entirely. Others have also tried this and some have failed.
Even better, though, is what I have been doing for the last 18 months or so: I ditched the bubble mailers in favor of cardboard DVD mailers ($5 for 25 at Wal-Mart). Cards get the standard sleeve/top loader/team bag plus a decoy on both sides and I seal all sides of the mailer with packaging tape after writing "Do Not Machine" on both sides. I put a Global Forever stamp on it (currently $1.15 IIRC) and a 21-cent stamp on it and drop it in the mailbox. Well over 100 of these have been sent out now to several different countries (closer to 200) and I have had no returns, no postage due (and no Customs forms to fill out). For larger lots or slabbed cards, I mate two of the mailers together and send it out for the "large envelope" rate plus a 21-cent stamp. This helps me keep shipping fees down for my foreign friends and customers (I charge a flat $2 on eBay auctions).
This may not work for everybody, but it certainly has been working for me, so hopefully this helps you at least a little.