• Camilles main strength is, her long range, diving threat
• And her burst threat, especially in early game
  • (technically she retains that burst potential through the game, but with less resource on support you won't, if not for a heavy lead)

So what's the conclusion here?
First, we need to be able to survive the initial wave of damage we'll encounter after engaging.
Second, we want to be able to expand and carry our early snowballing lead for as long as possible.
In essence we need to balance defensive measures with enough damage to keep our burst potential high.

Also our first item will arrive between 10-20 min (depending on how drastic of a lead you've gained already), so we need our first item to cover both bases, as especially the defense becomes important in team fights, but without early damage it's gonna be hard to build/retain a lead.

It's also important to build lots of CDR/AH to make the most of Camille's kit, and have Q up consistently in fights.


So let's take a look at our options:

Sundered sky Decent mix of stats, covering all our bases, HP, AD, AH. But it's passive is more tailored to shorter trades; having a 10sec cooldown and not enough healing to compensate for it, in a dive scenario.

Sterak's gage Again decent stats, but we're missing CDR/AH in return we get tenacity, also a stat we want but not as important. And the main caveat is that it's passive shield scales for bonus HP, therefore it gains a lot of its strength when combined with other HP-Items; so not ideal as a first.

Trinity Force Two major caveats here: We don't need the AS as we pick HOB as our keystone, and don't rely on CS. Bloodsong already carries Spellblade, so the game won't let you build Trinity on top of it(and Bloodsong's "value for gold/ gold efficiency" is far too good to be passed up on).

Death's Dance We get: 60 AD, 50 Armour, and 15AH. Plus the important part: it's passive, which perfectly covers our dive-protection needs. "30% of all physical and magic damage received gets spread out over 3 seconds. If any enemy you damaged dies within 3 sec after you damaged them: the stored damage won't be applied and you heal for 75% of bonus AD over 2sec." So when everything goes smooth and your team follows up quickly you get a slight heal between 40-120HP and ignore 20-30% of damage received.

Let's make a quick comparison what this means in practice:
Let's take a scenario which is favorable for Sterak's as a alternative early-burst-protection. You are lvl 11, 5/1/3(KDA), you will have ~1630HP (no additional HP from Items). The shield you gain from Sterak's would be 306HP, to put this into perspective:

• Your passive gives you a 406HP shield, in the same scenario.
  
• Or in % of max HP, Sterak's gives a 19% Max HP shield (of 1630HP so without Sterak's additional HP, because this makes for easier comparison).
  • But keep in mind this is on a cooldown after one time use, other than DD whose effect scales with a continued fight.
• So immediate gain is a 19-(X% - later in the game) shield from Sterak's Gage, and 20-30% damage being soaked up from Death's Dance (in both Cases, under ideal circumstances).

But this is where our second item comes in:

Endless Hunger 65AD, 20 Tenacity, 16-27AH, and 5% omnivamp Plus an additional 15% after our first target has died. So we get the damage to continue our lead, the AH we would have to buy Spear of Shojin for, and the tenacity from Sterak's Gage, plus 20% Omnivamp, which allows us to heal up again after the initial wave of damage, and therefore let's us get more use out of Death's Dance, as we can get another Cycle out of it's passive if the fight continues.

But you'll see the pattern here this build is better, but snowball dependent to actually excell. But with the massive damage from Hail of Blades early and Camille's excellent roams, you should be able to archive a lead most of the time.
And if not, you can just pivot after Death's Dance, it's still a great item if followed up by Sterak's Gage, or Sundered Sky if you don't need more burst protection.

For the rest of the build the logic follows: pivot to defensive stats to not lose your lead. And if your not able to convert your lead to a early win: you will be set up to do your job of engaging for your team consistently, as you now have the necessary defensive stats.
If you notice that you won't be able to close out the game early, go for a resistance item 3rd like Force of Nature and follow it up by Guardian Angel. This is the most optimal pivot to then retain your ability to dive. Later you can then also sell Endless Hunger for Sterak's Gage (or other defensive items).

Conclusion
Late game this build will be worse than the meta build. But that's the point if we want to make the best use of Camille support we should play for an early lead, to closing out the game fast. Playing for lategame, fights the constraints put on us by the support role (eco) and I think, is a relict from recently converting her from her other roles (top/jgl); if you look back, variations of "my" build(which followed the same build-philosophy), have been run on Camille support all the way back in 2022 when Bloodsong wasn't even a thing. The same build-philosophy worked best back then, and still does today.