Gazz,
To cut internal threads to match your spindle, the best way would be to get a 1/2-24 National Special tap, which is available for under $5, plus shipping:
http://www.sjdiscounttools.com/han1446.html
You can make a bushing adapter without using a lathe.
This is how I would try to make a bushing adapter, from 1/2"-24tpi to 5/8"-16tpi (as suggested by 1yesca):
1) Screw a 5/8-16 bolt into a chuck with that thread and cut off the end of the bolt almost flush with the back of the chuck.
2) Tighten the chuck jaws down onto the bare threaded spindle of the drill press so that the chuck is upside down.
3) Put a center drill in a vise on the drill press table, and run the drill press to make a hole in the bolt that is now in the chuck. Gradually increase the diameter of the drill bit until you get the tap hole size for about 50% thread. This ensures that your hole will be close to centered.
4) Put the tap in the vise and thread the inside of the hole, turning the spindle pulley by hand to drive the tap.
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Another way, if you use a taper mount chuck, would be to tap a hole into a piece, put that onto the spindle, thus converting the drill press into an upside down vertical lathe. Use a flat file to cut down the JT33 taper stub. This might be tedious.