She was sleeping, he woke her up at the point when he wanted to kill her. He held her had gun point she had little choice but to comply. Very few people actually attack someone holding agun on them trying to disarm such person and it is harder with a rifle because the person keeps you further away than a handgun does.
In the meantime he also could have threatened to hurt the boys if she didn't comply. Even if they were already dead she didn't know it.
After being shot the first time she raised her right hand to her wound which resulted in blood getting on her outer palm/wrist and running down her arm to her elbow. She wasn't unconscious at the time the shot was fired quite clearly though the shot could have rapidly sent her into shock. Jeremy freaked out because she was still moving and jammed the gun into her chin at that point and fired again killing her.
This explanation makes the most sense to me. I always thought Bamber must have gone to the boys bedroom first, then moved onto Nevile & June's room but finding Neville aleady awake and semi prepared for him, having been awoken by the muffled gunfire next door perhaps. One of the things that did go right for Jeremy was not waking Sheila up, although it wasn't make or break to his plan provided he was swift with the others.
The choroform would have been a great idea, except I can't see Jeremy with his big mouth keeping it quiet, as someone above mentioned. He would have needed to ask around for something like that.