Typically when see those two holes it requires a mating spanner wrench to unthread the cover. That cover should expose a ring of bearing balls so be careful not to spill them. You could use a couple of drill bits that match the diameter of the holes placed none threaded portion up and then use an adjustable wrench to fit around the shank to twist. Most people would take a nail set and hammer to them to get it to unscrew.
I would suggest you try turning without the mandrel by placing a dead center in the headstock and a live center in the tailstock. Using only enough pressure on the tailstock to get the blank to spin so that if you try to hold the blank it will resist and continue spinning. Turn as usual using sharp tools and light cuts. The blank may eventually stop when turning the piece and that just requires to tighten the quill on the tail stock a bit again.
Measure the hardware and then match the blank turning to that measurement.
If the bushings you are using have a step that will fit inside the tube then use those with the centers but normally bushings to be used with a mandrel will be straight pieces that just butt up against the ends of the blank and require the mandrel to keep them centered on the blank.
