pot ash is best added to compost but will be fine spread over the soil.
Rather than burn the paper, causing smoke, you can tear it up, put it into a large container with hot water, swill it around every so often and it will eventually turn to mush. Dig a small hole and bury the mush.
I'd just snip off the bit with the name, address and account number on and chop that bit into small bits with scissors. Put it all out in the recycled paper bag.