I have broken 2 whole cars for spares and send the lot (apart from 2 items) via Interparcel. I am always extremely conservative on the size and weight of any items I send and without exception all items are picked up and delivered safely.
The only 2 items I sent through someone other than Interparcel were sent via Parcelforce.
1st, an intercooler, arrived badly damaged.
The 2nd, a pair of turbo elbows, vanished off the face of the earth!!
For your rear bumper I would put the size as 150x20x65cm and 3kg weight and wrap it well with bubble wrap and cardboard corners. (Your 80cm thick measurement is from wheelarch to number plate not the actual thickness of the bumper through any one section). This is the method I have used to send front bumper, rear bumper, bonnet, boot and spoiler, body panels etc. and all picked up and delivered without fail.