How do you know Sheila had gone to bed early? Surely that is an assumption and no more than your opinion? According to Pamela, who as far as we know, was the last person to speak to June and Sheila, she was very tired and was going to bed.
We don't know if she ever actually got into bed or slept. 
She was found bare footed in her nightdress. In other words the clothes she would have gone to bed in.
By 10pm she had been up all day, as stated by Bamber & other people who saw her. Bamber saying she was unresponsive at supper even on an emotive subject. So tired.
It is common practice for people to go to bed around 10pm. Unless night clubbing or doing shift work.
June told PB Sheila was going to bed at 10pm. PB again said Sheila was unresponsive on the phone, again showing Sheila was tired.
There is no evidence on her or her nightdress she had fired 25 shots, been in a big fight & been up all night moving around a big house.
Sheila was on Haloperidol & under sedation. So would be tired.
Everyone else in WHF had gone to bed. Either being shot in bed or Nevill being found bare footed in pyjamas.
There is no evidence to suggest Sheila had stayed awake between 10pm - 3.48am. It is likely she was out of bed for less than 2 minutes before Bamber shot her.