I have done something similar to this in a bedless lathe (really a cymbal-making lathe with a temporary 3-jaw chuck fitted it) with a 3.2m length of heavy aluminium tubing hanging out of the chuck. 300rpm or so. I was actually only abrading the tube, not cutting it.
Get hold of a little laser pointer – I found a cheap one on Amazon or Ebay, fitted inside a dummy bullet for lining up rifles, etc. – and mount it in your chuck (in your case with the laster pointing into the headstock, through the spindle bore and out the back). This will greatly help you line up your steady. You can also see how well aligned your chuck is while you are at it – does it project a spot or draw a circle on the wall when the lathe is turning? Though, with a cheap laser pointer, that error may be in the pointer itself.
I made a very simple steady from a couple of casters, some dexion and a lump of wood. I clamped this in a Black and Decker Workmate which allowed easy adjustment of height and left-right position and was also suprisingly stable. Hold a 1" diameter stump of whatever on your casters and align the steady it so the laser dot (or circle!) is central on the 1" diameter face. Ideally have the casters contacting the bar at 90 degrees to each other, 45 degrees either side of the underside of the bar. You may have to stagger them to fit on such a small diameter. Though it sounds like other people's ideas for a steady with more friction would work just as well.
You might want to run your cutting speed a little slower than usual just to be on the safe side, but I don't think you'll have too much trouble with 4.5' of 1" steel whipping around too much especially if you make a steady.
I would put the steady about 1/3 of the exposed length of the bar in from the free end.
Cheers, Matt.