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Healing Bomb is a splash weapon, so it would be a touch attack, and therefore armor/shield/natural armor AC don't matter.
I would have to overcome any of the target's touch AC bonuses:
It makes sense to me that their size AC is 'set.'
But can they will away their Dexterity to AC for a single attack? Or would it be for the whole round?
Which other bonuses can they will away?
I've seen this question before and wondered if a good house rule would be to treat the target as helpless. A helpless character is not defending, and in the case of a willing ally, in a similar fashion, they are not defending either. There is no bonus to the attack roll for a ranged attack, but the defender loses any Dexterity bonus to AC and, their Dexterity is treated as 0 (-5 Dexterity penalty to Armor Class). Thus the target AC would be touch AC, minus any Dex or Dodge Bonuses, minus 5.
As far as the other bonuses, I agree with Zachiel, while some are a bit more obvious than others, ultimately discuss with your DM.
I don't think I ever saw a rule about this, and I'd be happy of being proven wrong. If there's really no rule, it's all in the GM's hands, and this is how I'd rule it:
Some of those bonuses - dexterity, dodge, insight - represent the character actively dodging incoming attacks. It makes sense that the character is not using them against your attack, if they're trying to be hit.
Of course, which kind of luck would it be if it prevented you from getting healed?
Some modifiers, like size, makes them hard to hit, willing or not.
Deflection, Sacred and Profane hare harder to adjudicate - and I've seen DMs houserule that Sacred and Profane should not be allowed to cohexist. Ask your DM.
Under the RAW for "Throw Splash Weapon":
A splash weapon is a ranged weapon that breaks on impact, splashing or scattering its contents over its target and nearby creatures or objects. To attack with a splash weapon, make a ranged touch attack against the target.
The RAW makes no distiction between a ranged touch or a melee touch:
[T]he attacker makes a touch attack roll (either ranged or melee).
Hitting an ally with a ranged touch attack allows them the opportunity to declare themselves to be a willing target:
Declaring yourself as a willing target is something that can be done at any time (even if you're flat-footed or it isn't your turn). Unconscious creatures are automatically considered willing...
Seeing as willing is the equivalent to the "Helpless" condition:
A helpless character is paralyzed, held, bound, sleeping, unconscious, or otherwise at an opponent's mercy. A helpless target counts as having a Dexterity of ZERO (-5 penalty [to their AC])
So, then, an Alchemist can throw healing bombs at their allies with minimal effort, only needing to account for size and (possibly) Luck.
As an aside, a thrown splash weapon can even target empty grid spaces at DC 5.
I believe, if the target is willing they can pass on any kind of saving throw.
If you did want to roll for it I would guess you would have to add significant bonuses to the roll considering your target actively wants to be hit by it.
EDIT: Here is a link to a forum that explains what I said better http://paizo.com/threads/rzs2pq2m?Hitting-friendlies-with-ranged-touch-attacks
some helpful posts include
Touch Spells in Combat: "You can automatically touch one friend or use the spell on yourself, but to touch an opponent, you must succeed on an attack roll."
There is no equivalent listed for ranged touch spells. Many people will allow the target to voluntarily deny themselves their Dex bonus to (touch) AC, but again, the rules do not directly support this.
