A question I was asked a while ago:
Why was Ripley's nose bleeding? was it an accident after she grabbed Ash in the computer annex?
No, the scene where Ripley enters mother was originally at the end of an unfilmed action sequence that was to take place after the disappearance of Dallas. Her nosebleed has been put down to many reasons by many people.
The unfilmed scene I mentioned is the infamous 'Airlock sequence' Parker sees the Alien outside the main airlock door. Quietly, he calls for Ripley over a wall communicator. Ripley and Lambert arrive on the bridge in time to hear him. Parker asks Ripley to open the airlock door slowly, as she does a green light is lit, and the Alien moves towards it with curiosity. Parker orders the outer hatch opened, but before she hits the switch a klaxon sounds startling the creature. As the inner hatch closes it traps a piece of the Alien, the Alien struggles but manages to break free causing acid to start eating away at the airlock door.
The outer hatch is still open while the acid continues to eat away at the inner hatch door, the Alien then bolts off towards Parker, who gets knocked over by the Alien and rendered unconscious. Ripley heads down to the airlock to help Parker, while there the hole in the inner hatch has totally opened up. The air begins to rush out the compartment begins to depressurize. A cylinder has been trapped in the emergency door so air is still rushing out. Blood begins to froth out of their nose and ears.
June 1978 script excerpt
Afterwards, Lambert arrives with Ash to give them oxygen and aid them. Both Ripley and Parker are half-conscious and in bad shape. Ripley accuses Ash of setting off the Klaxon. Ripley intends to prove it (another unfilmed sequence). She gets the key to mother and works away on proving Ash was the culprit. Still feeling the effects of the depressurization her nose continues to bleed, hence the blood during that scene.
The bridge segments of this scene were filmed, so with the intention of this scene being filmed. They continued with continuity of this sequence until the scene was filmed, that's why Ripley's bleeding nose was added to that particular scene. In the end, budget constraints and other miscellaneous reasons prevented this sequence from being finished.