Ripleys Bloody nose

It's possible that they needed a point of reference that segways into Ash's own version of 'bleeding' as it were so it is inferred that Ripley gets emotional and perhaps as a result tends to suffer nose bleeds from time to time. That plays out nicely as a counter-point when contrasted to Ash's 'head wound' finally revealing itself for what it is and his 'blood' starts to trickle down the side of his head, there is intermittant cuts in the edit between both him and Ripley. It's also possible that there were some additional moments that occurred during the filming process of those particular scenes and they were cut down to the bare bone essentials and we have to take it as a given and on continuity bais that somewhere during those moments of terse exchanges, prior to Ash's outburst Ripley just suffers a nose bleed and the rest plays out as it does.

She actually gets a nosebleed in every Alien movie. In Aliens it's after she defeats the Queen, in Alien3 she gets one during the memorial/cremation scene & in Resurrection she gets one after playing 'tag' with Warrick Brown from CSI.

Her nose is bleeding because in the previous unfilmed scene they try to jettison the alien out of an airlock, they pin it's limb which gets torn off and it's acid blood eats through the bulkhead doors and temporarily decompresses that part of the ship, Parker and Ripley are caught in it.