I support
Bulletproof, but it can only work if we remember to give our CAP great physical bulk and poor special bulk. Likewise,
Intimidate is a good choice, but, on the contrary, we need to give our CAP a lot of special bulk. Otherwise, the CAP will fall apart by either not helping our core or being too good. For that reason, although they are both good abilities, they cannot be combined, since both conflict with each other when it comes to choosing the CAP's base stats. I still think Bulletproof + Physical Defense is best for it, since the majority of the Pokemon we want to threaten are Fairies (which we already deal well with), Aegislash and Gengar (which Bulletproof deals with unless Gengar has Thunderbolt, but we should make our CAP weak to Thunderbolt as has already been stated), and Physical threats.
So, basically, I support Bulletproof and I support Intimidate, but I do not support Bulletproof + Intimidate.
Ground types are still a big problem though, which is why
Levitate is a good option. It doesn't help against Aegislash, but if we make it into our secondary ability and make Bulletproof into our first, it will potentially scare both Aegislash and Grounds, which I don't think is possible with only one ability.
Serene Grace could also a decent option for Grounds, this one more offensive than defensive. Unfortunately, Serene Grace Scald might just be too good, and not only against Ground-types. And besides, I don't think most Ground-types will want to switch in on the CAP in the first place.
The strongest argument for Serene Grace, in my opinion, is Azumarill, who will not want to swich into Scald or Lava Plume, earing the 60% Burn chance. But then again, Will-O-Wisp already threatens Azumarill, so Serene Grace ultimately doesn't seem that necessary.
I also don't think
Regenerator is a good idea at all, since Latias is supposed to be an offensive Defogger, and Luacrio also deals with Stealth Rock very well. The fact that our Cap is weak to Rocks is a feature, not a flaw. Regenerator just doesn't give Latias a strong reason to run Defog like we want it to.
For that same reason, I really like the idea of
Multiscale, since it forces hazards to be down to work, but if they are, out CAP can deal with Aegislash and Bulky Grounds in one fell swoop. However, Multiscale may be a little overpowered, and if we do give it to our CAP, we need to refrain from giving it any reliable recovery.
In any case, I think we can all agree that a defensive ability is best for taking on Aegislash and Landorus-T and the like. I'm not really convinced on any offensive ability so far.
Except for the fact said defogger isn't exactly one of the best in OU, as she's extremely vulnerable to Deoxys, Tyranitar and Bisharp, i.e. pokemon that dominate the entry hazards game in this tier. That, and the fact Latias faces huge competition from Latios for that role. Besides it isn't mandatory for Latias to be played as a defogger, since she can run other sets like Healing Wish and Calm Mind. We're all aware that Regenerator is more than a cushion against SR, but you're kidding yourself if you think it's not the main reason it's being considered here.
No, Latias
is one of the best defoggers in OU. Of the two Pokemon you listed, Bisharp is mostly countered by Lucario, Tyranitar hates Lucario unless it's scarfed, and Latias is not "extremely vulnerable" to either Deoxys formes, only really fearing Knock Off. Sure, Latias doesn't necessarily deal well with Deoxys-S, but it's much less a threat to our core than to, say, a Terrakion / Latios core.
And it actually is mandatory for Latias to be a defogger, since this CAP was explicitly supposed to support the offensive defogger version of Latias.