The biggest butterfly of a Reagan demise, IMO, was that he was kind of carrying the battle flag for neoliberalism in the late 70s. He was an ideologue about that, in a way that Bush wasn't.
I get the impression that Bush Sr. really didn't care about the domestic economy, and would have gone with whatever his party or advisors said. He famously wasn't about "that vision thing". By the late 80s, early 90s, the Republican Party was all aboard the neoliberal train, so Bush went with it. But if you drop Bush in office in 1981, I don't think he continues forward with Reagan's deregulation and deficit-spending plans. Not to the same degree.
Neoliberalism ended up being a blowout success in the short run, and after Clinton brought the Democrats on board, the US basically ran on a left/right neoliberal economic consensus. If you butterfly Reagan out of there, I'm wondering if that never forms. Maybe you see a continuation of the economic New Deal Democrats? That has huge implications for the next 30 years.
As far as how Bush would handle the Soviets... that's the last thing I would worry about. He was a foreign policy expert. I had read a long-form interview from Dick Cheney about assembling the coalition for Desert Storm behind the scenes, and it was amazing how much respect Bush carried. Both among the leaders of different Arab states, and inside the US military.
Bush didn't have Reagan's level of personal relationship with Gorbachev, and likely never would, but he was pragmatic and very, very capable. He would've kept the US military re-build going (can't see him getting on board with Star Wars, he was just too small-c conservative for that), and would have been a safe pair of hands to manage anything the Soviets wanted to try.
I would see him remaining pretty hostile towards the Soviet Union. As mentioned, he couldn't thread the Reagan needle of "I like you, but I'm still willing to nuke you." He would have leaned more on the latter, massing the US war machine and arming Afghanistan under the table. If Gorbachev was willing to play ball for de-escalation, he would be willing to play too, but I don't see him starting that initiative himself.