You can use the bushings you already have if they within close tolerances.
The only problem with mandrel bushings is that some are made Out Of Round or the center is drilled off center by even a very small amount - in which case it would have been noticed on mandrels too . JohnnyCNC made some bushing that were dead on accurate. Others make their own bushings out of different material. If you lathe is in perfect alignment, you can make your own by using calipers for measurements. I have some of JohnnyCNC's and I also use standard mandrel bushings without a problem.
I just realized that some of my old worn out bushings that I sanded down too much during my learning process - these work fine too with the mandrel-less process because I now rely on calipers for 'sizing' rather than the bushings. The inside of the older worn bushings are still within tolerance and so is the part of the bushing that butts up to the tube, so no need for new bushings.
Don't forget that once you get the blank down to within a mm, you take the bushings off and put the blank direct on the drive and live center for finish sizing/sanding and finishing.
The only extra tool you will need is a dead center to use in the head stock.
Grizzly sells dead centers here:
(MT2)
http://www.grizzly.com/products/Carbide-Tipped-Lathe-Center-MT2/H7967
(A list of dead centers here)
http://www.grizzly.com/products/searchresults.aspx?q=dead center