He would have to run fast Adam otherwise there would be blood stains from her bedroom all the way into her parents room. Perhaps JB assumed the police would assume it was Crispy walking around 
Bamber would be aware he had to be fast.
Blood would have been more of a stream running down her neck. So would have taken time to drip.
My view has always been Bamber woke & lead Sheila a few feet. Then took her by surprise.
If Sheila did wake & get out of bed, Bamber was ready.