Bairstow - Never been to Yorkshire have you? They think they are a country by themselves. Not playing cricket is a crime enough at any level, but playing for somebody other than Yorkshire would be a shooting offence. Seeing a Yorkshireman in the IPL when Yorkshire are playing any form of cricket is as likely as Kim Jong Un having a cuddle with Trump.
Broad and Anderson are under orders to rest from the ECB. Broad played Big Bash as he had 6 months off, unless the ashes tests are done next winter I can't see him repeating it.
Jason Roy gets in the region of £180k from England, probably £70-100k from Surrey, Big Bash plus endorsements. The £123k he gets from IPL benchwarming is very nice but I imagine it's not life changing. Most International cricketers in England earn £700k + endorsements, so unless you are Ben Stokes it's more about playing than the money. That said I imagine Stokes would also like a bit more time at the crease as well.