It Is possible to fly around the earth without adjusting your altitude, bearing or speed (if you had sufficient fuel)
I'm not a pilot but I have the basic idea. Don't take me to literally because you have to understand the basic concept I'm trying to get across.
Again you say "bearing", which is almost always refering to a compass.
But I understand what you're saying.
You're claiming that if you fly in a perfectly straight line - "straight as an arrow" - you would be able to fly all the way around the earth and end up back where you started.
The problem is that you're basing this claim on the assumption that the earth is a sphere. If the earth isn't a sphere, your claim is quite simply wrong. Since your claim is dependant on the earth being a sphere, you can't use it to prove that the earth is, in fact, a sphere. You'd have to verify your claim some other way - probably by actually doing it - and that's really not possible.
Bearing to my understanding can refer to the direction someone is heading.
The problem is,
You can circumnavigate the globe. It is possible.
It has been done.
Therefore I am correct, and the Earth is in fact not flat.
(Not necesarily a sphere, but definely some sort of shape similar to a Sphere)
Heading due east in any applicable form of transportation for a long enough time will put you back in the same general area (if you don't run into any land masses)
You don't need to do any crazy half-assed experiment which isn't applicable to finding the shape of this planet, or you can just agree to give up your simply baffling beliefs and go with logic.
Specifically based on the fact that people have/are/will go completely around the Earth.
So it's not flat.