Listen son.
I preach a slow-walking, spacing, patient, opportunist Bowser. A Bowser, I believe, should take only calculated risks while controlling as much space and covering as many options as his Bowser-ness allows. Through his defensive perseverance and reading of his opponents options, the humble Bowser main will pivot grab his victory with the blessed spin-to-win followups bestowed upon him by Sakurai, and make swiss cheese of his opponents dreams with the Up-Smash that will clank the heavens.
However, there is one exception to this personal Bowser philosophy of mine. As you can guess, that exception is the Shiek matchup, in which a radical kind of mindset is required.
Although I will explain my reasoning, I believe this video conveys the general kind of strategy and approach that Bowser relies upon in this matchup:
https://www.youtube.com/watch?v=050XUPFDzSc
Upon the realization that you are fighting a matchup in which you are forced to approach at all times against a character who has such an advantage in frame data that if unplugging your opponent's controller were legal, the Shiek player could still probably plug it back in in time to f-tilt you for 30 damage, you can't go into it with ideas of "baiting out moves" or "winning neutral" or "limiting options". None of that **** matters when you're fighting Shiek, because none of those things are ever going to happen even against a mediocre Shiek when you are playing Bowser.
No, victory for Bowser in this matchup happens for a much stupider, meta reason.
Having selected Bowser and pushing start when you see that your opponent is Shiek is where your mindgame starts. If the Shiek player is familiar with the matchup at all, then it's actually even better because then he is more likely to go into autopilot Shiek mode knowing how easy-bake oven Shiek wins in neutral against Bowser. The more comfortable the Shiek is, the better, because we are by no means going to win if the Shiek is taking you seriously for all of the match.
When the announcer says "Go!", that's your queue to push the control stick quickly in the direction of the Shiek initiating that screen shaking Bowser run, while having your index finger primed on shield anticipating needles. If you are ever walking while Shiek can throw needles at you, you are doing it wrong. When you are within boxing range of Shiek, try not to use shield even if you think she'll SH fair you. Fortress is good for beating aerials, and in general you just want to beat her attacks with yours, creating a wall of hitboxes. If you're on Smashville, my favorite thing to do is to jump immediately on that platform and fall in with an attack or Klaw-to-Fortress. It's a terribly stupid thing to approach a Shiek with, but that's actually the point.
There is no point to playing this matchup as anything but Bowser Approaches Shiek with Hard Reads And Gets Hit A Lot While Trying. It is how it is, and every moment you hesitate in accepting that is more needles and less pressure on the Shiek. So you just go in. You just do it. You start playing like an insane person in hopes that you can eventually read the Shiek's movement's well enough to get a punish that smarts. And with Shiek, you only need like three grabs before she's dead. You'll get hit a lot. In fact, if you get grabbed or faired, don't even airdodge or jump, just DI out to ledge and get back into onto the stage without dying. In fact, against Shiek's nair or bair, at low percents Bowser tends to just eat the move and has frame advantage on hit, so there's just another reason to not play defensively. If you want to experiment with this, try crouch canceling her aerials and d-tilting, I'm curious about it.
And let me reiterate; You are reading the Shiek's movement. Not an option. Not a reaction. Step 1 is pick a general space where the Shiek will be in 1 to 2 seconds upon your approach. Step 2 is decide if you should throw a hitbox or a grabbox. Over the course of the game you should know to mix these up, but in the beginning just make a guess about the Shiek player's personality. Is the Shiek dodgy, and doesn't like staying in one place? Run in, Fortress. Is the Shiek stubborn, and prefers to stay in one place, thinking that he can just punish everything you throw at him? Just run up and punch his shield, grab if you're really feeling it. Step 3 is do it. Dropkick the air where may jump. Pivot grab the space where he may roll. Empty hops into grabs. SHAD Klaw. SHAD Fortress. You know how it goes, you play Bowser. Do all of the stupid things that you normally want to but aren't supposed to. If you guess wrong, it's fine. You're Bowser, you'll live to 200 and she'll live to 80. You have twice as many chances to guess right, and she doesn't have kill confirms anymore.
All of this relies on the premise that the Shiek doesn't adapt to your reckless strategy in time to take advantage of it. Regardless of percent, if the Shiek is somehow reacting to your approaching, you're winning and you can find that grab that will kill. As soon as she understands what you're doing however, she'll take advantage of it with needles and fake-outs and you'll be forced into approaching carefully again, which inevitably ends up with Bowser getting grabbed more often and slapped around.
If this works out for you, the match will be very short and make the Shiek player feel like garbage for losing because of a few lucky hits or sick reads.
However, it goes without saying that this is one of those ideas that are just stupid enough to work. So don't take this advice as sound. But if you are going to go Bowser against a Shiek that knows what they are doing, the most optimal strategy is for Bowser to reduce the game to a series of rock-paper-scissors interactions in which his rocks are harder and his scissors cut deeper and the Shiek player can't wrap his head around it.