An A320 Captain reported that the crew failed to select the engine bleeds off for a BLEEDS OFF takeoff because the First Officer was starting an engine; they were dealing with complex BOS taxi requirements; and experiencing fatigue.

Narrative

We briefed a Flaps 2; TOGA; BLEEDS OFF take off from Runway 27. After takeoff; we noticed that we had forgotten to select the engine bleeds off. I believe two items contributed to our omitting to select the engine bleeds off as we had briefed. 1. As BOS was using Runway 27 for takeoff; I elected to do a single engine taxi to conserve fuel. Taxiing from our gate to Runway 27 involved crossing 3 runways and a taxi route that I was not very familiar with. While we remained focused on the taxi route and coordinating clearance to cross the 3 runways enroute to Runway 27; we also became distracted from our bleeds off SOP set up. As an additional distraction; the First Officer was also tasked with starting the number 2 engine while backing me up with the taxi route. 2. I also believe that fatigue was a contributing factor in our SOP omission. This was day three of a trip with a wake pattern of early; early; and earliest. Day one involved a XD:00 domicile time wake up. Day two was XD:15 and day three was a XA:45 domicile time wake up. While I felt fit to fly; I also felt tired from the very early wake up on day three. I will try to be more careful and deliberate with SOP compliance and give more consideration to minimizing distractions; especially when fatigued in the future.