I think you should take some pride at riding so hard that your legs burn when you're finished, at age 65 no less. I think the burning is just a natural result of pushing yourself and extending your fitness up to new levels. So you've done the work needed to get nice and sore, that's the difficult part. I see the fun part as afterwards, when I can gorge on food and have an excuse to be lazy and lay around a lot.

I see muscles burning from riding a bike as being no different from the burning you get from lifting weights, running, hiking. If you're still sore the next day, maybe take a quick 10 minute spin around the block in very low gears. That'll help.

Good food, rest, a little stretching, and father time are really all you really need. And once you recover, you'll notice some real fitness improvements resulting from all that pain. Good luck, and keep those wheels turning.