I've done this loads of times Jeff.
Some bezels are tough to get off, some really easily pop off. It all depends on the retaining wire.
Around the edge of the crystal is a thin groove in the metal case. Inside the bezel is a similar groove, which houses a thin hexagonal (or more sides) wire. This wire clips into the groove into the case and holds the bezel in place. If you have a loose bezel you can slightly bend the wire upwards, so it is held tighter to the case.
In the flatter area of the case are holes (usually 3). These house a tiny tube with a spring loaded ball bearing (like a biro). These push up onto the notched underside of the bezel, which makes it click around.
These notches vary depending on the job of the bezel. The gmt's have more spaced out notches so that the bezel jumps every hour per click.

This is why the plastic bag is needed, as the wire or spring loaded bearings can sometimes fly off in all directions!

Stewart

: I am either: a coward, too protective of these old watches, or
: both of the above, so I have never tried this. Still, interested
: to hear about the results of this attempt. Plastic bag?

: Jeff