Well the Soviet Union really are not the bad guys in the Bond series. They are either not Soviet at all or rogue soviet agents working against both the West and the USSR. I can't think of a bond film where the Soviet government is the major antagonist. Interesting, Fleming created the criminal organization SPECTRE for his stories because he believed the Cold War would in the early 60's so having the USSR as the bad guys would make the Bond series obsolete.
In 1986 the USSR made its own action movie, The Detached Mission, about Soviet heroes trying to stop a crazed Vietnam veteran from launching a nuclear war. The American villain is backed by businessmen based in "Florida" (filmed in Cuba).
hi! you may be interested in several previous threads on this or closely-related topics. The posts don't discuss Soviet reaction to American portrayals particularly; they more describe Soviet depictions of Cold War themes.
I'm not entirely sure this is the correct sub to ask this but, did the USSR (even modern day Russia) make films where the USA/UK were the 'Bad Guys'? this thread contains a round-up of several posts (including the above), and some additional discussion.
We had a "Red Dawn"; was there ever an equivalent (White Dawn?) in Soviet pop culture?
lastly, this post gives an overview of the FAQ section What did the Soviets think of the Cold War: Compare/Contrast the Soviet Union's internal use of Propaganda to the US's internal use of Propaganda during the Cold War
if you have follow-up questions on locked posts, ask them here and include the relevant user's username to page them.
Just thought I'd drop in and point out that that James Bond movies are not American action films. They are British action films.