what overseas bases?

The USSR fell because of rampant military spending, up the 30% and potentially more according to Gorbachev.
All hidden as "industry" so it looked like they had low amounts of military spending. But yes, their problem was the private sector wasn't private, it was hypermanaged and ultimately not given room to grow or innovate. They employed people but didn't always pay them, they made things they didn't necessarily need, they built cities they couldn't maintain.
They were desperately afraid the West would invade the USSR, while also being afraid of rebellion and coups in the home country, leading to a really fucking economic profile and lots of distrust at the higher levels. Stalin's ridiculous paranoia certainly didn't help either.
The fact of the matter was the Reds didn't have that big of an economy, nor a particularly stable one, and the industry they did have suffered heavily in WW2.
US industry grew stronger ten times over and showed no signs of slowing down. It could create more tanks with a smaller budget than the Soviets could, and that scared them. Not to mention the US had the lion's share of good scientists and the funding to get them to work, and the Soviet scientists were by no means bad, but they were outnumbered and could only dream of the funding the West was handing out. They fell behind technologically, economically, and as the Cold War dragged on they began to lose influence as well. Vietnam was probably their biggest success but it cost them dearly in funding and weaponry and ultimately did nothing to hurt the US in the then and now. If anything the lessons learned in SEAD and counterinsurgency and battlefield weaponry application only served to help reform and strengthen the US, while the Soviets only learned of how ineffective their advanced SAMs were at stopping US air domination and how their fighters couldn't actually stand toe to toe with US fighters.

The Cold War was a clash of economies and the US's economy was bigger and better.