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The IS in the 100-400 is about as old as it gets. It takes a while to settle down when first initiated and you should allow at least half a second for this and preferably a full second (because it is so slow). However, you can speed up the process by having it already running, which you can achieve by half pressing the shutter button or the focus button (if AF is not assigned to the shutter button) for just a moment. It will then stay active for a couple of seconds. Keep tapping that button and the IS will stay active. You do not need to be aiming at the bird when doing this.
Of course the AF will also become active, but chances are that you have not yet aimed at a target. However, that's ok because with just a momentary press of the button it will not try to track whatever it was pointing at. i.e. it will not keep trying to focus on your foot
When you do want to track the bird and you already have the IS running then it is time to take careful aim with your desgnated primary AF sensor (often the central one but you may select any AF sensor in some modes). Then (and not before) half press the shutter button (or press the AF button) and this time don't release it. The IS will settle very quickly because it was already fully active and the AF will begin tracking what you were pointing at, with the added advantage of a stabilised picture. Release the shutter when ready.
More modern lenses - i.e. just about every other IS lens except the 28-135 IS - will have a faster-settling IS. Some will completely settle in as little as half a second. It's a shame that Canon have not at least put a more modern IS processor in the 100-400L and called it a mark II because that could be done without changing the optical formula at all.
Note that when you look through the viewfinder the IS will seem to be effective much faster than one second after starting it but a photo can still capture the minor adjustments that are being made.
Also note that the AF tracking in AI Servo also benefits from having time to gather it wits before you shoot. More accurately, it gathers data about the speed of approach of the designated subject (whatever you had the designated AF sensor aiming at when you first started the AF, which is why getting the initial aim right is so important) and that is used to adjust the predictive AF so that the lens will be on target when the shutter is actually released even if it wasn't quite on target when you started pressing the button. Predictive AF data is trashed the moment you release the AF button no matter how briefly you do it, and will need to be reaquired if you still want to take a shot, but releasing it gives you the opportunity to re-aim.
In case it hasn't registered yet, the AF will have trouble locking onto the subject if the IS is still messing with the image as it tries to get its electronic "gyros" going, but once the IS is working correctly it will present the AF with a more stable image to work with.
And a final note; the AF of the 100-400 benefits from a decent camera. Back in the olden days I found a big improvement at focus tracking with a 1D2 compared with the same lens on a 20D. The 1D2 AF could cope with a faster frame rate than the 20D could because its AF system was able to get the info it needed and process it between shots to keep it on target. If your camera can't do that then you can choose a slightly slower frame rate to give the AF more time between shots to look at the subject.