Name:Advisor's Chambers
Type:Location
Expansion set: Here to Serve
Affiliations(s): Martell
Text:
Any Phase: Kneel a Learned character to stand Advisor's Chambers. +2 Influence.

If I want to play Westeros Bleeds, can I kneel Advisor's Chambers firstly, then Kneel a Learned character to stand Advisor's Chambers, then kneel Advisor's Chambers again to pay for the 4 influence cost of Westeros Bleeds?

Sadly no, there is no influence "pool" in the game like there is for mana in MtG. All 4 influence for the 'Bleeds would need to be knelt simultaneously before you triggered the location.

Look at it this way: say you have an event that says "kneel 2 Noble characters to...whatever." Can you kneel a Noble, play Distinct Mastery to stand it, then kneel it a second time to finish paying the cost? Of course not; because you cannot interrupt paying the cost for Effect #1 with Effect #2 - intended to help you pay the cost of #1.

That's essentially the same thing you are trying to do with your "kneel a Learned character to stand an influence source" and continue to pay the price of Westeros Bleeds.