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I retracted my fangs, pushed away the clone that hung from its feet in the centre of the room Wouldn't it swing right back? Unless it's on some track, like bodies in a morgue, or something. But we get no indication of that and looked at Conrad’s worried face.
“What is it?” I said, wiping blood from my mouth with the back of my hand.
The drip-drip of blood from the clone to the space-station’s floor filled the silence, while Conrad’s mouth opened and closed like a blat-fish.
“Say it again,Conrad," I prompted, "but actually speak out loud this time, so I can hear [what you are saying] you."
Conrad was young, semi-colon at least that’s how I thought of him. At only six billion years old he was half my age, !! When does this story take place? The title says at the end of time, but clones, space-stations and especially people named Conrad all sound like late twenty-first or maybe early twenty-second century. Since the universe is only 13.7 billion years old, either your vampires came into existence when they had nothing to eat, or the story is taking place billions of years from now. In the latter case, I would expect the surroundings to be unrecognizable and though there were a few beings older than us—two hyphens for em-dash, but here I think you just want a comma we were the last of the vampires.
“I said,” Conrad burbled, “That according to my calculations the

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Otherwise, good hook.

Thanks for the comments.

Yup, I guess it would swing right back, and no it's not meant to be on a track or anything, however a step forward should suffice to solve that problem.

When is this taking place? I generously figured the universe would continue for at least as long as it has been, so I was aiming at the reader assuming from the clues that it was in about 12 billion years time.

Would it be recognizable? NO...if it was a serious story, I would understand but this is going to be a story with a humorous edge. It is also going to be short. This story works better(due to how the story develops) with the retro-feel, IMO--as these guys are shortly going to try samples from their collection of the finest blood they have come across kept in bottles, samples from all sorts of creatures and aliens, while they wait for the end of time to hit....like a wine tasting.

These guys have avoided dying by avoiding the living...using fairly basic (but still sci-fi) tech. The names are to emphasize the stories comedy edge.