IS has to spin up when you first press the shutter release part way, because it is stationary to start with. Once it has spun up you can keep shooting in burst as long as the camera buffer can take it, the IS is constantly adjusting the whole time. There is no need for it to spin up between shots so long as you have the shutter release down.
There is no problem leaving the camera in burst mode, even for single shots, so long as you don't mind that you may sometimes inadvertently take two shots instead of one (depends on the fps). Just be aware that if you are concentrating on only taking one shot, you may get slightly increased camera shake as it can lead to less smooth action on the release, as you try to press and release quickly, rather than gently squeezing and only releasing when the shot is taken.
Generally though, it is fine to keep IS and burst mode on. That is my natural situation much of the time as I shoot action with big lenses.