"Bushism" and "Trumpism" only mean something concrete to very vocal (and very annoying) minorities. The GOP is, at its core, a vehicle for maintaining class hierarchy to whatever extent seems reasonable/stave off excessive leftist redistribution actions (i.e., "economically conservative") and maintaining societal norms and cohesion to whatever extent seems reasonable/stave off rash and flavor-of-the-month cultural movements (i.e., "socially conservative"). Beyond that, it goes where the winds are blowing.
My prediction after Trump likely loses in 2020 is that the GOP will try to dress a "moderately-conservative-but-still-minimally-egalitarian" economic package with a decidedly more articulate, less bombastic and unsophisticated version of social conservatism and traditionalism. You can support upholding our immigration laws and defending traditional American cultural norms without sounding like a yokel, and you can support maintaining economic stability without being a Randian who doesn't care for anyone but the 1%. Think John Kasich, without the current flare for anti-Trump-related attention.
This mentality will set the gop back
It's actually the only way forward.