Bush wins Texas and maybe Mississippi but loses some Upper Midwest states depending on how he responds to the changing face of conservatism, but otherwise, there wasn't a lot of time to step out of Nixon's shadow. He would be pretty similar to Ford, Rose Garden Strategy and all.
Not even sure he would win Texas. HW was never really seen as a "true Texan" the way his son would be. Despite his nominal home state being Texas, he came closer to losing it in 1992 than any Republican, including Trump in 2020, has since Ford lost the state in 1976. I'm not convinced he would have enough of a home state advantage there to overcome Carter. And I doubt it even more in Mississippi, which basically came down to racial polarization narrowly favoring Carter due to higher-than-average support from rural whites on top of high black turnout for him (this just barely changed in 1980, which is why Reagan just barely won it and it thus trended left despite the massive nationwide Republican swing).
He almost definitely loses Michigan, Iowa, and Illinois, maybe also New Mexico, Oregon, and California, so yeah. I think ultimately electorally Bush would have probably been a worse candidate than Ford in 1976, with or without the "Rose Garden strategy." Ford was more likable even if Bush may have been perceived as more competent. Bush also may have been more divisive among both Republicans and the general public, having at one time supported abortion and been opposed to the Civil Rights Act. He likely would have been skewered by the Carter campaign on such issues.