Yes, they are usually biennial, although sometimes they can be tricked into flowering the same year if exposed to several hard frosts at planting time.
I've never had them get bitter.

Thanks, Slimy!

Well, I missed my window of opportunity, and they were bitter today :(.

I cut them all, and stuck them in boiling water for 3 minutes. Still bitter. But 4 minutes worked :).

They have made lovely large beets, and I m still wondering if I'm doing the right thing, leaving them in the ground in hope of more leaves (which will presumably make the roots woody and icky),

Thing is, I still have beetroots in the fridge from the winter crop...

I have noticed that catalogs sell beet varieties that are mainly for the greens. For my beets I do several sowings during the season. You could have fresh tender greens in a few weeks by sowing the seed now.