Generally we say 'ベッドで寝る’。If you want to emphasis on 'bed', then you can say 'ベッドに寝る’。
For example, when you go to the hospital, a nurse says ’ベッドに寝てください’。
’ベッドに寝る’ doesn't short sentence of ’ベッドに入って寝る’.But normaly we think it means ' ベッドに入って寝る’。I hope you can understand it!