I am thinking about traveling from the south rim of the Grand Canyon to Las Vegas via Bryce and Zion. How long do I need allow for each park to make all that extra driving worthwhile?

As much time as you have; you can't spend too much time there!

One day at Bryce and two days at Zion.

Each COULD be visited in a half day if you barely leave your car, but both are BEST experienced by walking on a trail for an hour and leaving 90% of the tourists behind. Bryce should be seen at both sunrise and sunset for instance, and its amphitheatres should be walked into. Zion should be viewed from the top of the valley as well as its bottom, so a hike up the canyon is most useful.

The amount of time spent in Bryce depends on how much hiking you want to do. I could spend 3 days there easily.
Don't forget that the rim of Bryce is about 8,500 feet and you will feel the shortage of oxygen when you walk uphill unless you are in very good condition.
Good skiers don't have much trouble.

Zion, in my estimation, is worth one full day, which means two nights, with arrival early enough on the afternoon of the first night to take a good look at the visitor center exhibits and become oriented. If the place captivates you, 2 full days in the main part of the canyon might be worthwhile.

I like Bryce better than Zion, and would schedule more time for Bryce.

I agree with the above posters, unless you have at least a couple of days or more I wouldn't bother with all that driving. Just wait until another time when you will have more time.