Gibraltar delays?

'Is the border delay also causing delays for buses traveling in/out/through La Linea?' I cannot be sure what is intended here by 'bus' or what you wish to understand, but no bus crosses this border.

I have no recent first hand experience but I see no pedestrian queue metres from the border on this web cam - http://www.frontierqueue.gi/ I cannot believe the traffic queues back up affecting a bus entering or exiting La Linea.
And you are talking of two months time.

We parked in La Linea and walked across, which was easy. The traffic at the border is backed up in the best of circumstances. There is always a somewhat tenuous relationship between Gibraltar and Spain, sometimes the politicians get worked up about it, most of the time they just ignore each other. If you are on a bus, I wouldn't be surprised if your bus ends in La Linea. If that's the case, I'd walk (or taxi) rather than trying to connect to another bus into Gibraltar.

You might be better to check again a week or so before you go. Right now things are very tense and the Spanish have been purposefully causing delays. I'm not sure if that affects pedestrians or just vehicles, but the situation is dynamic and what is happening now won't necessarily be happening in a month and a half. And frankly, this forum might not be too helpful since you'll need up-to-date info - not someone that visited last year. Try the tripadvisor forums, which have more recent s from people that have recently visited (they are indicating few or no pedestrian delays right now).