Sense of balance degrades with age, supposedly starting around 25 years. We are told that it's due to changes in muscle strength, joint flexibility, decreased reaction time, and susceptibility to inner ear issues. Not to disregard all of that, but I think that there can be long periods of disuse, where we aren't really using much balance beyond the normal activities and we experience some loss due to that. I cite that balance improves with balance exercises, even simple ones like standing on one foot. If the simple training of balance improves it to a significant degree even at advanced age, I submit that the problem is due at least in part to lack of utilization.
In the case of feeling unstable on the bike while turning, I personally would be more concerned with the perceptive side of balance. Inner ear, vision, etc.