The photos in this thread were taken from a hide. I used a beanbag on the window sill to support the camera, more flexible than a tripod. Had the camera set on shutter priority 1/1000 second and Al servo.
You are right. Bean bags can be more flexible, if you can find somewhere to set them. They are also much easier to carry on a walk than a tripod or monopod. I have managed 8 miles with a monopod mounted to a camera and lens combination with total weight of about 5kg. You don’t want to do that many days in a row, but the results are worth it.
Shutter speed of 1/1000 should stop motion blur from the camera and you wouldn’t need image stabilisation on. Small birds can move incredibly quickly though and I have had birds blur themselves at 1/2000. On the other hand I have achieved sharp shots at low shutter speeds in low light if the bird decides to stay still.
Have you tried removing the focus from the shutter button and assigning it to a button on the back of the camera (if the camera allows this)? I have found this gives greater control and was recommended this by professional photographers. It can take some getting used to.