What is the pressure/force sensor used in the Beddit?
It's likely a flex sensor, or force sensitive resistor.  These are long devices that change resistance according to the amount of flexure (flex sensor) or force applied (force sensor) along the tape. If this is the case, you can measure the resistance, and should find that it changes as you bend or put pressure on the tape. Breathing and movements aren't very quick actions, so there's more than enough bandwidth available in such a sensor, and they are very inexpensive and fairly durable. Flex sensors are typically more stiff, and only respond in one bending direction, probably requiring two for this type of application (unless the instructions have a distinct "up" side for the sensor placement), so it's more likely a force sensitive resistor.

Here is a force sensitive sensor that closely matches your description:

Interlink model 408 FSR with 1/4-inch x 24-inch sensing region: