The distinction that matters most here is between a plain adjustable bed and a true home hospital bed: hospital beds are built around caregiving and safe transfers, with height adjustment, side rails, and a frame that can take the load of someone leaning on it. Given your mom's back problems and the narrow doorway, bed height adjustment for her sake may be the deciding factor rather than the head elevation. For 8-12 weeks, rentals are common, and Medicare Part B can help cover a semi-electric bed when a doctor documents medical necessity, but you'll typically pay a monthly coinsurance. Worth asking the social worker to specify that paperwork.