A perplexing case, to be sure. Either a well orchestrated “hit” arranged by someone who had a good reason for wanting her dead or just a deranged “fan” who just happened to find her there when he did. There is no obvious motive for someone with the wherewithal to arrange such a hired hit. But, it is not beyond the realm of possibilities. I am inclined to believe it was just a random obsessed fan and BG certainly fits the profile.
Still, in light of the very little time Jill spent at that flat and the randomness of her comings and goings, it would seem so improbable that he would just happen to be there with a gun when she arrived unless he either had some advanced knowledge that she would be there or he invested a great deal of time “laying in wait”. How would a stranger know when she would be there? Yet, waiting around in an urban setting should attract attention. I can not see how anyone could have spent any significant time, waiting for her to come or go, without someone noticing and later reporting it. It is unlikely, but possible, that he didn’t have to wait long or otherwise went unnoticed.