Trying to understand floating voltage
Usually a raw AC power feed is grounded on the neutral wire and, if tapping off a voltage via a variac, you are "keeping" one wire tied to earth. This is because variacs do not isolate. Adding a bridge rectifier to the output isn't a problem but earthing the DC output of the bridge rectifier is because you end up with a diode that is from the "hot" feed (as opposed to the neutral feed) that gets blasted with a lot of current 50/60 times per second and destroys.

Just draw out the circuit and see. Use an isolating transformer for safety, peace of mind and protection for the diodes.