Top left: David Bowman is 'ejected' from his EVA pod into the emergency airlock of Discovery One. Top right: Bowman then careens across the airlock at a high rate of speed, and hits his head on the opposite wall. Above left: We observe that Bowman's breathing is irregular and his body motions are lethargic while he's disconnecting HAL. Above right: Bowman experiences deviated gaze while in the 'stargate'.
Bowman's symptoms after hitting his head (lethargy, irregular breathing, and deviated gaze) indicate that he's suffering from a subdural hematoma (also known as a subdural hemorrhage), which is a type of traumatic brain injury. Subdural hemorrhages may cause an increase in intracranial pressure (ICP), which can cause compression of and damage to delicate brain tissue. Subdural hematomas are often life-threatening when acute. Acute bleeds often develop after high speed acceleration or deceleration injuries and are increasingly severe with larger hematomas. The mortality rate associated with acute subdural hematoma is around 60 to 80%. [a] Note that most of the airlock wall is padded, but that Bowman has hit his head on an unpadded portion of the wall. Also, he has hit the top of his head, which is why we don't see external evidence of an injury, since any bruising or rupture of the skin would be covered up by his hair (and then later by his space helmet after he puts it on).
A few seconds after Bowman has hit his head on the airlock interior, he has no visible blood streaming down his face. His head injury is more internal than it is external.
A few seconds after the above view, the camera cuts to HAL (below left) for a few moments, then there is a fade to Bowman wearing a space helmet (below right). Again, we can't see any external evidence of an injury - if anything has begun to develop or collect on the outside of the top of Bowman's head by this point, such as some matted blood, we can't see it, due to the fact that he's wearing the helmet.
Much later than the above, while Bowman is standing in the 'hotel' room after having passed through the stargate, there is still no visible blood on his face. This is because, again, the actual injury he has suffered is mainly an internal one; any external blood has not collected in an amount sufficient to start running down his face.
a. Wikipedia, 'Subdural hematoma'. Web, n.d. URL = https://en.wikipedia.org/wiki/Subdural_hematoma.
