Delta
We use the APU with X-bleed in AUTO. We only use x-bleed starts if the APU is inop. Normal SE taxi out is with #1 Bleed ON, X-Bleed OPEN, and APU Bleed OFF. This allows the #1 engine bleed to supply both packs, and (the book says) this keeps the engine exaust from contaminating the air conditioning via the APU intake/bleed, which is why we don't turn the APU bleed on until right before the 2nd start.
From our Manual:
DELAYED START PROCEDURE:
ENG MODE selector: IGN/START
Cross Bleed Selector: Rotate Auto
APU Bleed pb: ON
Engine #2 Bleed pb: Verify ON
Y ELEC PUMP pb: OFF
Engine Start Procedure: Accomplish
After engine start:
ENG MODE selector: NORM
APU BLEED pb: OFF
ENG ANTI ICE: as reqd
APU MASTER SW pb: OFF (may remain ON for MDM considerations)
Flight Controls: ckd
DELAYED START checklist
Hope this helps.