Okay, I'm just popping in from the Bowser boards to give some input. I hope you guys hear me out. Here comes the massive wall of text!
I can imagine that some people believe that the matchup is something like 70-30 in Game and Watch's favor. His advantages over Bowser sound pretty solid on paper. He's freakishly strong, he has fast attacks, lots of range, lots of priority, he's near ungimpable, and the turtle totally *****. How can Bowser, a character that many people don't even take seriously, compare to that?
First of all, I'll say this about Bowser. He's a turtle, pun intended. Most Bowser players literally live inside of their shields. Spot dodging and rolling is not something that Bowser players do on reflex, but shielding is. Shielding for Bowser is like spot dodging for ROB, that's how much Bowser needs the thing. Bower also deserves some credit for having the biggest shield in the game, meaning that he can actually absorb things like Turtles fairly easily without getting stabbed. Hell, he can even absorb Nados with the thing.
This is a matchup where you need to space well. If you do not space well, you will lose, simply because Bowser punishes improperly spaced attacks with such incredible ferocity. Improperly spaced Turtles and Fairs will be met with a Fortress OoS, which is one of Bowser's most well known tricks. The Fortress is by far, one of the best special moves in the game, and for good reason. It comes out fast, since the hitbox appears on frame 6. You can't hit Bowser during the startup time either since the Fortress has invincibility frames on frames 1-5. That makes the Fortress an ideal countering move for nearly any improperly spaces move. If the Fortress hits close to Game and Watch, it'll do upwards of 15 damage, and knock you away from Bowser. It's important to note that at higher percentages, the Fortress can be used a a surprise killing move if you're not careful. While it's killing power is still inferior to it's Melee counterpart, it's still a viable killing move out of a shield. To put it simply, if you're above 95%, make sure you choose your attacks carefully, otherwise it might spell death for you. Make sure you space your turtles and Fairs well, otherwise this fight will be very annoying.
Like I said before, you must space properly to avoid the Fortress. However, even if you land outside of the Fortress's range, still has ways to reach you. His Jabs come out as fast as the Fortress does, and they have as much range as hit Ftilt. Even if you land outside of Fortress range, Bowser can still start jabbing like a madman and possibly reach you with it. Another attack that can be used this way is the Klaw, which is one of Bowser's best attacks. As you probably know, the Klaw is a grab, but it's comes out fast (8 frames) and it has very deceptive range. It has the ability to kill, but mostly it's used for damage. Doing 18% a pop is pretty deadly, especially if you're light like Game and Watch. Which is why I say again, spacing helps this matchup from being super frustrating.
For the third paragraph now, I'll say it again. Space well. If you're using the Turtle or Fair, they try to hit him with the end of it. In fact, it would be best to stay as far away from Bowser as possible in this matchup. Bowser's fast ground game combined with his OoS tricks really screws Game and Watch up if you try the direct approach. (Which you shouldn't be doing anyway, because you're Game and Watch.
) Make sure you try and time your aerials to reduce their ending lag as much as possible. A mistimed Fair means enough lag for Bowser to get one of his Dash Grabs in. While Bowser will have difficulty grabbing a competent Game and Watch, you still must be careful to avoid Bowser's grab as much as possible. It's not Bowser's throws that you should be worried about, since he lacks anything deadly like Game and Watch's Dthrow. However, Bowser has another trick up his sleeve; grab releases.
As many people now know, Bowser totally ***** out of a grab. That's because due to some bizarre programming oversight, Bowser recovers from grabbing 10 frames quicker then everyone else. That means that Bowser gets 10 free frames to do whatever he wants to Game and Watch if you get released on the ground. This sucks, a lot. If you get released on the ground, Bowser can keep grabbing you again, and there's no way to escape if Bowser's timing is perfect. Bowser can essentially pummel Game and Watch for quite a bit of damage this way, which is why you should try to jump out of Bowser's grab as soon as possible. However, it's a bad situation either way. You see, if you get a jump release on Bowser, Bowser can abuse those 10 free frames even more.
When you get a jump release, Game and Watch will suffer 50 frames of immobility, while Bowser will only suffer 20. That means that Bowser has half a second to attack Game and Watch while he's floating in air. This puts Game and Watch in a very bad position, since Bowser can jump and Klaw Game and Watch this way. (As always, 18% is not cool.) If Bowser has grabbed, or chaingrabbed Game and Watch at the ledge, then Bowser can even Fair out of a jump release, which can be dangerous if Game and Watch is at high percents. All in all, try your best to avoid the grab. Bowser's grab range isn't that impressive, so avoiding it shouldn't be a big problem. However, it's always important to know how much **** Bowser can do out of a grab. Doing upwards of 35% from a grab is somewhat that you need to watch out for, especially since Bowser can pull out killing moves from his grabs. Which is why I'll say again, you need to space yourself. Getting close to Bowser means it's that much easier for him to land a grab.
Oh, and beware of Bowserciding. If Bowser grabs you near the ledge, then he can grab release into a Klaw, which is a potential suicide. Always DI toward the stage, or it's a free kill for him. This is important to note because Bowser's grab release chains into a Klaw so easily, and since your jump release moves Game and Watch a considerable horizontal distance, it makes it even easier for Bowser to land a successful Bowsercide on you. Not something you should worry about too much, just be careful.
Beware of Bowser's edguarding game as well. Bowser's moveset is tailored to edgeguarding pretty well, and he has lots of tools to utilize. Granted, it's near impossible for Bowser to gimp Game and Watch, but he can still edguard him all the same. (just with difficulty) Angled Ftilts come out surprisingly fast and have good range to them. Bowser's Dtilt does as well, and they both can hit you if you're not careful. Although it seems silly for me to mention it, take note of Bowser's Fsmash. Bowser's Fsmash has a really weird disjointed hitbox, so it can hit you on the ledge even if Bowser's head doesn't reach it. You'd be surprised at how many surprise kills Bowser can get simply because people don't know that the Fsmash is heavily disjointed. Really, it has longer range they Marth's Fsmash. Just look out for it and try not to get predictable with your approaches. Well spaced approaches can actually be stopped with a well placed Fsmash, simply because the hitbox is so outragously huge. And of course, as you know, the Fsmash usually means death if it hits. You shouldn't see it much, but it's still a move that's very usable for Bowser. (I actually think it's his best smash, if that's saying anything.)
Do not expect to gimp Bowser in this matchup either. I'm not being overly optimistic about Bowser's recovery either. Bowser is simply a character that is much harder to gimp then most people believe. Yes, his recovery follows a very predictable trajectory, but it actually pushes Bowser a very considerable distance. Because of the high amounts of priority the Fortress has, as well as its invincibility frames, Bowser's Fortess can go through a lot of things as long as it's used with proper timing. Once, I managed to avoid a Wario Waft edgegaurd just because the invincibility frames of the Fortress cut right though it. Not a likely scenario, but it's definitely possible. If Bowser is getting gimped in this matchup, then he's doing it wrong. Well timed Fortesses can be Bowser's answer to like, everything.
And the final thing I'm going to mention...Bowser's Utilt. This move is godly, and probably one of the best Utilts in the game. First of all, the Utilt comes out fast so it's not very telegraphed. It also kills early, and is one of Bowser's most usable killing moves. If you're above 90%, then it can kill quite easily fresh. One of the things that makes this move so awesome is that it has lots of priority and an extremely bogus hitbox. The hitbox for his move is so weirdly disjointed that it even outrages and beats all of Meta's aerials. For God's sake, beware of this piece of crap. It can even go through Turtles, Fairs, and Nairs if you're not careful.
So yeah, that's all I have to say. I actually believe the matchup to be 60-40 in Game and Watch's favor. Sorry for all the text. ><