As a physician I can say that such injury as we've seen here with one's ear and part of the skin from the back of the head to be completely torned away would result in a massive bleeding and pain shock, that normally would keep away an individual from continuing his actions. Will you be able to talk much about business after having you leg broken just a minute ago?
However, and it is not rare, that immediately after suffering a serious injury patient is able to continue acting like nothing happened and even claiming of feeling no pain at all. This is due to the traumatic shock affecting each of us differrently and heavily depending on a seriousness of injury (for instance if he had his limb torn off or smashed, he would have felt unconscious for sure because of excesively strong pain impulse, which can not be processed by brain. As a result the brain simply "turns off"). If this is the case then Bishop could withstand this trauma just with a slight grunt and then continue chatting with Ripley at least for a couple of minutes before he would actually feel the pain.
As a science fiction fan I have another possible explanation for this: in a distant future when medicine and technology are far more advanced, people could make some biomechanical advancements to themselves, such as artifcial organs or enhanced vision, etc. thus improving personal abilities. Considering his age maybe Bishop have had half of his body being replaced with artificial parts including skin and ears
This would explain some odds with his exterior look after being hit.
