On my press, each of the axles supporting the casters is individually adjustable.  If you look closely at the picture below (click on it for a larger version), you can see that the axle is machined slightly off center from the hole in the chassis.  Thus, when the axle is rotated in the frame, the caster is raised or lowered.

 

To prevent the axle from rotating during use, the axles at the 4 corners of the press can be locked into place using the set screws shown below.

 

Each axle has a couple of holes bored in it.  One hole takes a cotter pin used to keep the caster in place.  The other hole is used to adjust the axle (see below).

The locking nut shown above requires a 1-1/16" wrench (a socket won't do since you'll want to hold the adjustment while tightening the nut).

My plan is to use the 2 center adjustments first, making sure that the bed ends up precisely parallel to the cylinder.  Then adjust the 4 corner casters to achieve a level bed that rolls smoothly back and forth.

 

To adjust the corners, I'll use a machinist's spirit level.  I'm not sure how best to adjust the center.  One idea is to use something incompressible, e.g., a block of steel, between the bed and the cylinder.  Another idea is to use a slightly shorter block of steel with a strip of solder laid on top.  Crank the combination through, compressing the solder.  Finally, measure the resulting solder thickness using micrometer.  I'll have to experiment a bit until I can develop a repeatable procedure.

 

It occurs to me that a well-prepared mechanic would use a feeler gauge.  Why don't I have one?

 

Ultimately, I used a combination of the above ideas, then made final adjustments by printing small examples (without ink) on each side of the the cylinder, visually comparing the depth of impression.