Something else not mentioned in the WIKI (US Postal Money Order - Bisq Wiki) is that you can buy a money order in other places than the Post Office. I usually buy them in a gas station. I pay in cash and they never asked for an ID. I think any Moneygram or Western Union also has money order to buy.
So my recommendation is to buy them there and then you can go to a post office (USPS, UPS, Fedex, etc) to send the envelope. USPS have an electronic cashier. I never used those but I think you can send an envelope without having to talk to a cashier (and present ID).
This should be the default method in US for Bisq.