How do I find the right hospital bed for my mother in assisted living?

An Occupational Therapist could give you a evaluation as to the best type of mattress. (A hospital bed, is a hospital bed it is the mattress that makes all the difference, although there are some beds that are specific for specific mattresses)
If the hospital bed is for "convenience" of the staff good chance is you/she will be paying for the bed. But if there is a medical reason for the hospital bed and specific mattress it will most likely be covered.
Mattresses range from a simple mattress to an airflow mattress to an alternating pressure mattress.
You should also ask about side rails. do you need full rails, one or two. Do you need half rails if so do you need 1, 2 3, or 4.
Rails will depend on if she is at home or in a facility. You can use full rails at home and use both, you can use 4 half rails at home. In a facility 2 full rails or 4 half rails are not allowed as they are considered a "restraint, or confinement"

You could ask for an OT evaluation. And keep in mind her long term needs, it's more cost effective to buy once than to have to replace/upgrade down the line.

Does your mom need a hospital bed because of her medical condition or because it makes it easier for staff to tend her needs or both?

I think the mattress is likely the more important factor.