I did not think that there would be a 1 second delay between wanting to Burst, and actually Bursting, because by that time you would have already been struck by the bamboo sword, or by the car that you were trying to stop and analyse in the first place.
then you are right, there is no delay between them, as shown multiple times already.
and nope, you are not forced to burst if someone close to you bursts... the only time you are forced into burst-mode is whenever someones challanges