A patient transferring bed assembly includes hospital bed that has a mattress deck and a plurality of legs. A gurney is provided that includes a mattress panel and a plurality of legs. The gurney is positionable in a transferring position having the mattress panel being positioned adjacent to and being oriented coextensive with the mattress deck on the hospital bed. A mattress is slidably coupled to the mattress panel on the gurney and a patient lies on the mattress. The mattress slidably engages the mattress deck on the hospital bed when the gurney is positioned in the transferring position and the mattress is urged to slide laterally onto the mattress deck. In this way the mattress transfers the patient from the gurney to the hospital bed without requiring the patient to be lifted.