IOTL the Warsaw Pact was disbanded, and Soviet troops were recalled from eastern Europe and elsewhere. But Nato continued, and the US maintained its military presence all around the world.
Is there any plausible scenario where Nato and Warsaw Pact are disbanded at the same time, and the US closes down many of its military bases around the world, while the Soviets do the same? Basically, a kind of mutual demilitarization? Was such a thing possible in the late 80s/early 90s (probably under a different President than Bush)?
NATO could be ended by recognising that it's reason for existence had disappeared.
It was created when Stalin was in charge of the USSR and had a huge army along the Elbe. 'Stalin had ten million men under arms in Europe' is how it keeps being quoted. Being afraid of facing the business end of guns controlled by Joseph Stalin was perfectly reasonable, and joining together for protection against them sensible.
Stalin had been dead for a long time in 1989, the Soviet Union was broke - hence leaving eastern Europe at all - and the security issues Europe might need to deal with different. Urban terrorism had been a huge issue in the 70's and still was in Britain. The PLO had a habit of launching terrorist attacks that affected citizens of European countries. Keeping the oil flowing from the middle east was in the interest of European countries, and relying on the US Central Command for that made them dependent on the good wishes of the US Government, which arguably undermines national sovereignty.
These issues were not taken into account when NATO was thought up. Disbanding NATO and working out a new alliance to deal with current and foreseeable issues would seem perfectly appropriate. The post-Ghadaffi civil war in Lybia, with its bombing campaign, that Britain, France and the US supported but Germany didn't might have been different if there had been a treaty alliance that required political consultation/agreement from its members.
Maybe Lybia would not be the mess it is today because the counter-arguments were taken into account. Whether or not to intervene in the Syrian Civil War was a question that affected European interests. Dealing with it at an alliance level is not an insane idea, but NATO doesn't really have provision for that.
So yes, dissolving NATO as soon as the Warsaw Pact collapsed is justifiable. It didn't deal with the security needs of the nations it was supposed to serve anymore.