I would pack any loose change so that the coins can't rattle audibly against each other or be felt through the sides of a bubble mailer.
USPS urges people not to send cash through the mail, so their mail handlers won't be tempted. It's rare, but I have heard of packages being stolen inside post offices. In at least one case, they eventually got the repeat thief on camera and fired his butt.
Many people use the Flat Rate Priority boxes so they don't have to weigh it and stand in line at the PO. Since all flat rate boxes have tracking numbers, I think they get lost less often. Certainly the boxes don't get torn up as often as bubble mailers.
With the flat rate box, the tracking and box are free, unlike bubble mailers. I used to use bubble mailers to save the dollar or so overall cost difference, then realized that I was spending money on gas, plus time spent in line at the PO. I might go back to bubble mailers after retiring, when a dollar and an hour will be closer in value.
