direction

It appears that you can take the Heathrow Express train to Paddington Station, which is quite close to your destination.

Definitely the Heathrow Express. Quick and easy. You can buy your ticket in advance in the US and either print it out or store it on your smartphone.

I had to laugh though, it took me longer to walk from international arrivals border control to the train platform than the actual travel time from the airport to Paddington Station took.

Bear in mind that the HEX is the most expensive train journey on earth. Heathrow Connect is cheaper and you could also do it by tube,

Princes Square is nearer to Bayswater Tube Station than Paddington. If you can manage your luggage on the tube that would be the cheapest option.

HEX is not the most expensive rail journey on earth. It isn't even the most expensive per journey length in London on standard rates, and you can get discounts routinely these days. Having said that, it may only make sense if you are saving time via the underground route though, which Bayswater may be with a bit of a walk.

I'm very confused.

You say you will be in Bayswater.

Yet in your other thread you say,

We will be staying in Abingdon outside of London about a hour bus ride

Now that really confuses me because Abingdon is a rural suburb of Oxford nowhere near London and much further than one hour.