Dubya sort of had one eye on the governorship for a while, so it's likely he runs in 1990. As just the son of a VP who lost a very winnable election he wouldn't be gifted the nomination though. The Bushes are not going to be establishment superstars in this TL.
I doubt Jeb would wait the better part of a decade before the governorship opens up, and the same applies to him in respect of primary politics as it does with Dubya. The Bushes are at a discount ITTL. Most likely he either goes straight in as a Congressman if he's serious about politics, or just drifts back into business.
In both cases, given how likely 1992 is to be a Republican year if Dukakis wins, and without a presidential name, I doubt either become president or even nominees.