I think the Royals’ decision not to invite the Bamas kind of precluded inviting other high profile Americans.
I’m sure the Bushes would have been invited, if it had not been for that. the Queen really liked President Bush.
With that said, the Bushes' have such class, that even if they had been invited I would bet they would have declined just on the basis of the Obama's not being invited --- of course that is just me.