About Appolonius ADV.

Appolonius effect is continuous: if the target of the bleed changes, his bonus bleed changes accordingly. It's the same as Constanza whose wording is being revised to: "Constanza gets +2 bleed against a Methuselah who controls a ready Ventrue." By the way, I'm puzzled that Constanza's current wording suits you, because "when bleeding" could be interpreted as a triggered thing.

Anyway, there's nothing here that indicates that he gets another bonus bleed each time the target of the bleed changes.

It's basically the same as "Appolonius gets +1 bleed against a Methuselah for each titled vampire he or she controls".

TheLich wrote:

Gets could simply be replaced with has and the whole potential for a problem is fixed. This game could actually use wording the differentiates between "triggered" abilities and "continuous abilities" to put it in Magic terms.

You can already spot them: "triggered abilities" use words such as "each time," "if", "when".
Continuous effects use words such as "while" or are simple statements, such as Appolonius's, or to take another example, Ayo Igoli's: "Ayo gets an additional vote for each ready titled vampire you control." (will be reworded to: "Ayo gets {+1} vote for each ready titled vampire you control.")