How can I come up with a cost for my deduction for donating a full electric home hospital bed?

Check on sites like Craig's List and eBay for identical items.  If your item is value is more than $500, you will need an appraisal for it.  Under $500, a receipt from the charity will suffice.

I have a fully hospital bed fully electrified

Please see the answer above.

if this was paid for, like Medicare or other insurance, then your cost is zero