I'm afraid that difficulty feeling good and performing well without a warm-up is common among older riders. As the saying goes: "By the time I'm warmed up, I'm too tired to ride!"
When we were young, we could jump off the couch and start playing pickup basketball or touch football with nary a stretch or jumping jack. That ability slowly deteriorates as we age into our 30s and 40s. By the 50s and 60s, a good warmup is crucial for any activity to avoid injury and make sure we have fun.
I'm not aware of any studies that have explored the relationship between growing older and warming up. Certainly as the population ages while still remaining active, there will be research that might show us how to warm up most efficiently.
Based on experience, the best warm-up for cycling is cycling. Here are 4 tips:
Start slowly and gradually increase your pace. When riding with others, look for a friendly wheel to follow to make the start that much easier.
Avoid group rides that go from the gun. An immediate fast pace can be hard for anyone who has driven to the start.
If possible, pedal to the ride for a warm-up or get there early enough to spin around for 15-20 minutes. An on-bike warm-up is essential before a race, of course. If the location makes riding impossible, take your trainer and use that.
Stretch if it works for you. The jury seems to be out on how effective stretching is for warming up. Studies on whether stretching helps prevent injuries are inconclusive. Some show benefits, others have found a higher rate of injury.
The consensus at this time seems to be that stretching after the activity is fine but it shouldn't be done "cold" before cycling, running or other sports. Of course, everyone is different. You'll find people of any age who swear by re-ride stretching.
Another strategy is to ride easily for 10-15 minutes to a grassy park or other place you can park the bike. Get off and do a short stretching routine before continuing. This might quicken your overall warm-up.
Bottom line: You're not in your 20s any more, Art. Avoid hard efforts and, thus, the risk of injury, before you are warmed up -- however long it takes