I got an email question the other day regarding warming up. This student said that it takes him about half an hour to get up to speed, and he wondered if this was normal. He also inquired about a good warmup routine.
A thirty minute warmup is absolutely normal, especially for adults who aren't as limber as the young whippersnappers (a.k.a. teenagers) who can just pick up their instrument and start playing full speed right off the bat. (The questioner was a little disappointed to hear that, actually. He was hoping there was something wrong that he could FIX!) It just takes a while for your fingers (and the brain) to get into gear and to start working simultaneously. If you're a long warmer-upper, it's important to make sure your practice session is longer than your warmup period. If you need 30 minutes of warmup, practice for at least an hour, because if you only practice that first half-hour, you've only shaken off the dust and cobwebs and you won't progress on your new skills or tunes. Anything you play within that warmup period, whether it's your new tunes or your old tunes, isn't really being practiced, it's just being reviewed.
Now, on to what you should warm up with. I'm in favor of warming up with old, familiar tunes. Play through "Banjo in the Hollow," "Cripple Creek," and all of those first tunes as your warmup. Start out playing them slowly and then gradually work up to your normal tempo. Some people like to do rolls as part of their warmup, but I've always found that boring. I do not have the patience to practice rolls. I've always figured that you use all of your rolls while you're playing tunes, so unless you're trying to work out a specific roll or a fingering problem, roll practice gets thrown in for free along with everything else. Your warmup period is also good for playing through all your old material. It is SO important not to let your older tunes slide in favor of piling on new material.
One further thought on warming up. If you know you need a long warmup, make sure you warm up before your lesson. If you only have a 30-minute lesson, then you barely have time to get comfortable with the banjo/guitar/mandolin/fiddle in your hands before, boom, time's up. Even ten or fifteen minutes in your car before you go inside will make a big difference when playing what you learned last week, and learning whatever is new for this week.