Crossing from Canada to the USA without a passport on public transit?

I'm making a new answer to add some color about specific points where I've crossed.

As the main operator of many routes, Greyhound's contract of carriage does not explicitly require you to have a passport:

Passengers must have proper travel documents which may be checked at or prior to boarding an international schedule and which will be required for entry into another country.

Obviously if the bus driver or station staff are checking before departure and interpret that more narrowly you may have a problem getting on the bus.

Generally, in my experience, the smaller the crossing, the more likely it is you'd get all the way to the border without the bus company checking your documents and you having to explain why the irregular documents you have are valid.

Canada / US Border crossings served by mass transit east to west:

• Montreal to Burlington VT and onwards towards Boston
  • Greyhound: the drivers sometimes check documents departing Montreal, I've also boarded without them checking. Buses cross at the Highgate Springs Port of Entry.
• Montreal to New York
  • Greyhound and Trailways buses to New York (Plattsburgh, Albany, NYC): early checkin is required and passport information is entered into a computer in the Montreal bus station and seems to be forwarded electronically to the border at the Champlain Port of Entry.
  • Heiman Bus operates a nightly bus service: it's rather informal and has been in trouble for not following regulations but is seemingly tolerated because it provides special "services" to the religious community including gender-segregated seating. No experience with this.
  • Amtrak: documents are checked when boarding in Montreal.
• Ottawa to Syracuse
  • Greyhound buses run Thursday and Sunday night. No border experience here.
• Niagara Falls
  • Greyhound run buses from Toronto to NYC. No experience here.
  • Megabus has routes from Toronto to Buffalo and NYC. No experience here.
  • Amtrak from Toronto to NYC. No experience here.
  • You can walk over the Rainbow Bridge in Niagara Falls. Greyhound, Megabus and GO Transit can get you to the Canadian side. On the US side, there is an airport and Trailways buses to Buffalo.
• Lake Ontario
  • Owen Sound ferries can get you from Leamington ON via Pelee Island to Sandusky OH. No experience with this one. There's no mass transit to Leamington, the nearest Greyhound stop is in Tilbury ON. Greyhound and Amtrak serve Sandusky.
• Windsor to Detroit
  • Tunnel bus from Windsor to Detroit: this is a regular city bus, nobody checks IDs until you get to the border.
  • Greyhound also runs from Windsor and other points in Ontario to Detroit. No experience with this.
• Sarnia to Port Huron
  • There's no official way to cross the border but by taxi as explained in a previous answer.
• Sault Ste. Marie
  • Bridge Bus from Ontario to Michigan. My experience was the other direction, it's a "normal" city bus, the driver didn't check anything. The border agent was a little surprised by a non-local on the bus. An airport and Greyhound serves the Ontario side - the Greyhound stop is far from downtown, you can take a city bus. Indian Trails bus connects the Michigan side - the stop is also a ways from Downtown but there is a sidewalk or it's possible to get use the Dial-a-ride service or get a cab.
• Thunder Bay to Minnesota
  • Happy Time Tours goes from Thunder Bay to Grand Portage MN. Use the dial-a-ride to get to Grand Marais. From there, once a week there is a connection to Duluth, plenty of onward connections from there. No border experience here either.
• Winnipeg to Grand Forks
  • Jefferson Lines restarted the bus in 2017, I can't find schedule information at the moment, may have been suspended again. No border experience here either.
• Vancouver to Bellingham and Seattle
  • Amtrak train - You are checked by US customs and immigration at the station in Vancouver, so you have a chance to talk to actual officers. You are also stopped at the border, but only briefly, to collect your paperwork.
  • Amtrak bus - There's no pre-clearance in this case so you'll clear the physical US border at the Pacific Highway crossing. The document check is not strict, but I'd avoid delaying the other passengers on the bus as everyone would have to wait for you to be processed.
  • Greyhound - no experience here.
  • BoltBus - You are checked by the bus driver, so you are likely to be refused if you have weird paperwork. BoltBus also runs on tight turnarounds, so I wouldn't expect you to have much time to make your case.
  • Quick Coach - no experience here.
• Victoria to Seattle
  • Clipper Vacations ferry. There is US preclearance in Victoria, seems likely you'd be able to get to the border agents there.

I took the Tunnel Bus. The driver did not ask any identification. I suppose that with such a local bus running back and forth all the time, it is easy for them to take people back if they are denied entry.

So, with the Tunnel Bus you need to convince only the border security.

Airlines will not let you board without the proper documentation, ie: passport, period, end of story. The reason being is that public carriers can get fined if you are not eligible to enter the USA and they transport you there.

Trains and buses are also public carriers and are supposed to document that you have permission to cross the border before boarding you.

The "I am a US citizen and you can't keep me out" line does not work for anyone except a US CBP agent. So basically you need to speak with a CBP agent and without a car you would have to walk to the check point and start explaining. But even they can make your life miserable and send you packing to the nearest Embassy or consulate to arrange a replacement passport before being allowed to enter, if they so decide.

Sneaking across the border or even being outside the country without your passport in the first place ... well as Forest would say "stupid is as stupid does".