With a bike, most of this conversation should be more centered around preparation long before mounting the bike.
The bike fit needs to match your current flexibility.
Then, you need to do whatever you need to do off the bike on a routine basis to be able to use that bike fit. Core work or cross training the supporting muscular structure.
Randomly stretching right before a ride? Most non-cyclists athletes actually use a bike as their "warmup". Look on the sidelines of an American football field. Or gym of other sports folks. They hop right on the stationary and spin for a bit to warm up. Then go on to the weights or sprinting or whatever they do.
If you have to do that before the bike, I'd say you need to roll easy around the block for a bit to warmup if anything before starting to go at it. But no need for a pilates class before a bike ride.
Maybe if you're a time triallist who has a pretty constricted bike fit and you've been on vacation.