What did the CIA think about the partition of Pakistan in 1971?

First of all, CIA is a part of the executive branch of the US government, and is subordinate to the US president. It's meaningless to speak of "CIA's intention," you should really be asking about "US presidential administration's intentions." From time to time, these are different from the ones by the US Congress (the legislative branch) and this was the case during the Bangladesh War of Independence. In view of the atrocities committed by Pakistan's government in East Pakistan, US Congress imposed an arms embargo on Pakistan in March of 1971. These were repeatedly violated by Nixon's administration.

Here is a quote from the Wikipedia article that you linked which makes the attitute of Nixon's administration to the situation quite clear and I see absolutely no reason to doubt it:

The US government stood by its old ally Pakistan in terms of diplomacy and military threats. US President Richard Nixon and his National Security Advisor Henry Kissinger feared Soviet expansion into South and Southeast Asia. Pakistan was a close ally of the People's Republic of China, with whom Nixon had been negotiating a rapprochement and which he intended to visit in February 1972. Nixon feared that an Indian invasion of West Pakistan would mean total Soviet domination of the region, and that it would seriously undermine the global position of the United States and the regional position of America's new tacit ally, China.

To demonstrate to China the bona fides of the United States as an ally, and in direct violation of the US Congress-imposed sanctions on Pakistan, Nixon sent military supplies to Pakistan and routed them through Jordan and Iran, while also encouraging China to increase its arms supplies to Pakistan. The Nixon administration also ignored reports it received of the genocidal activities of the Pakistani Army in East Pakistan, most notably the Blood telegram.

The Nixon administration was widely criticized for its close ties with the military junta led by General Yahya Khan. American diplomats in East Pakistan expressed profound dissent in the Blood Telegram. Nixon denied getting involved in the situation, saying that it was an internal matter of Pakistan, but when Pakistan's defeat seemed certain, Nixon sent the aircraft carrier USS Enterprise to the Bay of Bengal, a move deemed by the Indians as a nuclear threat. Enterprise arrived on station on 11 December 1971. On 6 and 13 December, the Soviet Navy dispatched two groups of ships, armed with nuclear missiles, from Vladivostok; they trailed US Task Force 74 in the Indian Ocean from 18 December until 7 January 1972.

The Soviet Union supported Bangladesh and Indian armies, as well as the Mukti Bahini during the war, recognizing that the independence of Bangladesh would weaken the position of its rivals—the United States and the People's Republic of China. It gave assurances to India that if a confrontation with the United States or China developed, the USSR would take countermeasures. This was enshrined in the Indo-Soviet friendship treaty signed in August 1971. The Soviets also sent a nuclear submarine to ward off the threat posed by USS Enterprise in the Indian Ocean.

At the end of the war, the Warsaw Pact countries were among the first to recognize Bangladesh. The Soviet Union accorded recognition to Bangladesh on 25 January 1972. The United States delayed recognition for some months, before according it on 8 April 1972.

What was CIA's role in this? Much of the documentation is now declassified, you can find it online if you look hard enough. Here is just one document:

From April 12, 1971, here, documenting CIA's assessment of the prospects for Pakistan in the conflict, which were estimated as bleak, but there is nothing to suggest that CIA analysts were in favor of not supporting Pakistan.

Another example: After looking through the throve of declassified CIA intelligence reports, Hindustan Times in the article here "Revealed: How CIA tried to gather intel before 1971 India-Pakistan war" concludes:

Contrary to the popular perception of the famed capabilities of the US spy agency, the CIA, had little intelligence or an accurate assessment of a crisis the American leadership was deeply interested in – the 1971 Indo-Pakistan war.

Kalyani Shanker, senior journalist and the author of Nixon, Indira and India – Politics and Beyond, said, “The myth that the CIA knew everything is not true. They knew something and something they did not know. For sure they did not know about the timing of the 1971 war. Both (President Richard) Nixon and Kissinger were taken aback when the war broke out in December.”

Records of another WSAG meeting provide an insight into the CIA’s thinking and how it was far from the reality. On August 17, 1971, Kissinger asked then CIA chief Richard Helms, “Do you think Indians will attack?” He replied in the negative. “My personal feeling is that they will not do so.”

By this time, India had nearly completed its preparations for war, which started on March 26, 1971.

There is some mix-up of the listed dates, since India openly joined the war only in early December of 1971. But, according to Wikipedia's article

As early as 28 April 1971, the Indian Cabinet had asked General Manekshaw (Chairman of the Chiefs of Staff Committee) to "Go into East Pakistan".

The linked Hindustan Times article also says:

On November 24, inside the Situation Room at the White House, Kissinger was evidently frustrated with the CIA. “Why can’t we find out more?” he asked. The previous day, the situation in the subcontinent rapidly deteriorated after Indian troops crossed the eastern border and Pakistan declaring a state of emergency in preparation for war. India neither confirmed nor denied crossing the border at that point in time.

This was despite the US keeping a close eye on the eastern border from 69,000 feet above with its famed U-2R ultra-high altitude reconnaissance aircraft since May 4, 1971, the documents reveal.

An option before the WSAG was to approach the United Nations, but the US did not have enough information. “The question is what hard data we have to support whatever action we want to take. We have no doubt that India is involved and that they are probably across the border. But we need something to nail down the exact nature of their activities and we need it in a day or two,” Kissinger said.

If you do not believe these documents and are still standing by Bezmenov's claims, you should explain why. After all, he was a KGB, not CIA's employee, so how come he knew more about CIA's knowledge of the situation than CIA's director?