Just time to build a bed base and assemble it. We inflated the bed to get the dimensions - 80" by 62".
Everything is 2 by dimensional lumber, originally in 8 foot lengths. The headboard and footboard are 2 by 12s, the side rails are 2 by 8s, and the cross rails and ledgers are 2 by 4s.
Off cuts of the 2 by 4 cross rails make the side ledgers - two to a side with a gap in the middle.
Side rails are connected to the head and foot boards with surface mounted bed rail brackets from Rockler. 2 by 4 ledgers are screwed to the side rails with 1/8" ply spacers behind, gapped at 11 1/2" on center from each end to half way along. Those gaps are made to take 6 sawhorse brackets (also from Rockler) with 1/8" play either side.
The brackets don't need to be screwed into place - just hook them over the 2 by 4 s.
The spacing of both the 2 by 4s and their spacers down from the top of the rail is 1 3/4", and they are about 1/2" short of the rail brackets at each end.
Head and footboard ledgers are made from the last two 2 by 4 offcuts, plus an odd bit of 2 by 4 I had spare. The screws in the rail bracket in the left of the picture below had to be loosened to get it to fit, then tightened. To make life easier I screwed the odd bit of 2 by 4 nearest this bracket so it could be removed to get at the bracket screws. You'll see a fixit block on the right end of the ledger, and there are two more underneath it. These make it easier to screw the ledger back in place after the bracket is secure.
The headboard and footboard have a foot at each end. These are pieces of 2 by 4, roughly 10" long, each held in place with a lag screw through the middle of the foot and washers, one under the screw head, one between the two pieces of wood.
These feet turn so they are at right angles to the boards to keep them upright while the rail connectors are fiddled into place. Once they've done their job you can kick them straight in line with the board, so they don't get in your way.
The sawhorse brackets drop in their slots and the cross rail 2 by 4s drop into them.
Finally a set of five 1 by 12 utility shelving planks are cut 1/4" short of the side length (so they don't bind) and dropped onto the cross rails and ledgers.
A furniture blanket goes on top and is tucked under the side planks. The inflatable mattress bed goes on top, and hey presto, you have a bed with a decent height. Even if the mattress deflated overnight, there is enough height for someone to get out of bed without too much trouble.
I will return to the mini bench soon, I promise.