What is this red dashed line between door and cockpit window?
(Source: airliners.net)

The letters read 'air bridge'. The line is used for docking with the air bridge as you suspected. Also see: What are these markings under the passenger door?


  (...) the position of the alignment marks are not standardized and are carrier specific.


It also appears on the silver livery:


(Source: planespotters.net)



It reminds me of this:


(Source: wikimedia.org)