I have a PO mail box and find that they DO bend bubble padded envelopes.
I use a 6x6" CD envelope - bought in bulk on ebay for 16 cents each. They cost 52 cents to post.
To insure the envelopes need to be at least 1/4" thick, I believe, so have heard of some putting a packing 'peanut' in, to make it thicker.
~Jillian
artist, Jillian Crider
... google me!