Rice was reportedly overheard saying, “As I was telling my husb—” and then stopping herself abruptly, before saying, “As I was telling President Bush.” Jaws dropped, but a guest says the slip by the unmarried politician, who spends weekends with the president and his wife, seemed more psychologically telling than incriminating. Nobody thinks Bush and Rice are actually an item. A National Security Council spokesman laughed and said, “No comment.”
One lesson Rice absorbed during the first Bush administration was that a personal relationship with the president mattered a great deal, and she forged her relationship with George W. early on. She and the candidate could talk sports--Rice was a big football fan and Bush a former owner of the Texas Rangers baseball team--and Rice could tell stories of baseball great Willie Mays, who had once been her mother's student in high school. George Bush was a fitness buff and Rice, who used more than one personal trainer, worked out with him. Among the "Vulcans," the self-styled coterie of Bush foreign policy advisers, Rice was the one who could explain issues in a way the candidate understood easily. "I like to be around her," Bush was quoted as saying, "Besides, she's really smart!" 
Slate had a pretty good take on the incident:
The great promise/major selling point of Socionics is the promise of true love in duality relations. Duality partners are very different kind of personalities and on a casual level understanding between duality partners is not always easy. Sometimes though duality relations flourish even between friends and colleagues. And conversely this kind of close personal working relations, (well what do I know), can help in identification by hinting at the possible types of the parties: in this case most likely between INTJ Rice and ESFJ Bush.
There does not seem to be any agreement on the type of the American president, (well there rarely is MBTI being little more than a collection of type descriptions.) In my opinion there are number of reasons why George W Bush is ESFJ. First the hard evidence, here is a picture of young George W Bush. The pictures on Filatova's page tend to be of youngish people so currently I can type young people based on their looks much better than mature adults. Compare young "Dubbya" to pictures of ESFJ men on Filatova's database here:
Can you see what I see? I hope I am not hallucinating... It is pretty crazy stuff this visual identification, but hey why not...
Then there is functional analyzis. I think we all quite familiar with quotes about incidents like this one:
It is said, that, before September 11, George W. Bush thought the Taliban were a Bavarian brass band. Now, thanks to his comprehensive knowledge, the most powerful man in the world has got into hot water again.
It was Condoleezza Rice, national security advisor, who helped her boss out of the embarassing situation. During a conversation between the two presidents, George W. Bush, 55, and Brazilian president Fernando Henrique Cardoso, 71, Bush bewildered his colleague with the question "Do you have blacks, too?"
Rice, 47, noticing how astonished the Brazilian was, saved the day by telling Bush "Mr. President, Brazil probably has more blacks than the USA. Some say it's the country with the most blacks outside Africa." Later, Cardoso commented that regarding Latin America, Bush was still in his "learning phase".
In other words logic is hardly his strongest function. On the other hand he has neither shown much hesitation in admitting his ignorance or his need to rely on his administration and advisers. This corresponds quite closely to white/introverted logic as weak subconscious fifth function:
The fifth function has great difficulty making sense of information on its own. Information is perceived on the one hand as little understood background noise and on the other hand as something of great importance. The individual feels good when others explain to him what he is experiencing in this aspect of reality and what he should do about it. One’s opinions in this area are easily influenced. Without others’ care and concern one feels like an abandoned child. A person rarely feels ashamed about problems related to his fifth function and can easily request help if he sees that others are self-assured in this area. If others speak with an authoritative tone, one listens carefully to advice having to do with one’s fifth function. One rarely stands up for the fifth function’s interests, but accepts as much help as others are willing to give. Criticism is interpreted as concern for one’s needs. People who lack duals’ concern in this area frequently hint at their fifth function’s helplessness and neediness in the subconscious hope that the right people will respond to their cry for help. Dualization helps to develop the fifth function and make sense of one’s subconscious needs in this area. Self-perfection on one’s own is extremely difficult. If the individual has someone he trusts to follow, he feels happy and protected. Otherwise he feels resentful of society at large for not providing him with the care and assistance he needs.
Going through all the functions and possible types would be rather painstaking exercise, but I think functional analyzes can be highly useful in typing people. Basicly for example this kind of open shameless demonstration of one's ignorance would generally be characteristic of only people with logic as third and fith function thus either ISFJ, INFJ, ESFJ or ENFJ, and methinks: much more likely the extroverted types.
On other hand there is ample evidence that extroverted emotions is the lead function that George Bush most identifies with, The first function is the strongest and most conscious function and forms the core of one’s perception of reality.
President George W. Bush: "I'm a loving guy... And I'm also someone, however, who's got a job to do... and I intend to do it." (Sept 13, 2001
Note also extroverted/business logic as role function: He works very diligently. He does not prefer one errand to another, all should be accomplished whether interesting or not. This is not something to be discussed or analyzed; simply the work must be completed (ESFJ decription)
This post became rather longer than I intented, I may continue later... But I think it pays to observe people carefully: to notice not only which functions are clearly visible and strong: but also in which aspects of reality do people openly demonstrate their weaknesses (fifth function) and which aspects of reality are perceived rather painfully and may elicit irrationally strong negative reactions (most often fourth function). I think it more should be written about the Socionics Functions. The problem with the functions in MBTI seems to be that they are kind of hanging in the air - there is no clear theory on how different functions should show up in people's behaviour. Thus the disputes over what the functions for different types are, easily seem rather pointless. Since the theory of functions in MBTI seems to rarely be able to predict anything, the usefulness of the whole theory is questionable at best - I for one have yet to read a single MBTI description of types according to their functions.
There actually seems to be an MBTI analyzes of George W Bush which favours ESFJ as his type, and at least extroverted feeling is well descriped, I could have added many more examples.