Depending on the size of the bed, the person in the bed could be in one of many different positions, so positioning it on the mattress could miss the presence of somebody. The only place that has to register all weight changes on the bed are the legs. So the best place for the pressure sensor would be between the leg and the floor. The previous is if a pressure sensor is to be used.
The alternative is to use a simple pull switch, as used over openings in burglar alarm systems. Several of these can be positioned across the length of the bed and connected in series, so if weight is applied anywhere along the length of the bed, one of the switches will be triggered. These switches can also be adjusted for sensitivity. To avoid causing discomfort the actual pull cord can be replaced with ribbon. If the base under the mattress is one of those interconnected spring versions, then the pull switch could be connected to a strategic position on the base, or a microswitch could be used to detect pressure on the base.