The bracketing feature essentially automates the "normal" picture taking sequence. The normal sequence is the user presses the shutter release, mirror lifts, shutter opens then closes (thereby exposing the sensor/film for the desired amount of time), mirror releases and comes down completing the sequence/operation. The bracketing feature, just performs this operational sequence for the number of times indicated in the bracketing setting - up to 5 (however adjusting the exposure settings [over or under exposed] for amount and type of exposure variation desired - up to +- 2 ev). So that is why you have the mirror "flapping". The two second delay, injects a two second delay right after the mirror lifts, so that the vibrations from the operation dampen out just prior to the shutter opening and closing.
The mirror up, essentially pulls the mirror up, and then executes the sequence - in that the mirror up command is in force, the mirror is never released, not allowing it to come down. With the mirror not being lifted and released the 2 second delay is no longer necessary to dampen the now non existent vibrations from the mirror not moving.
The other thing that you can do is to set "one push bracketing". What this does is normally, you need to maintain pushing (depressing) the shutter release (even on the wired remote) in order to take all x (2, 3 or 5 bracketed images). If you release the shutter button prematurely the sequence will stop short of the desired number of images. With "one button bracketing" set (page 159 of the manual), having to hold the shutter release down is no longer necessary. Just depress the shutter release once, and the 2, 3 or 5 images are automagically taken.
Also, normally the bracketing exposure are taken around the nominal 0 ev. However, by using the [+/-] button, you can introduce a bias, so that the bracketing is taken around say 5 frames taken around a +2/3 ev base (or what ever value you dial in).