Cathy,
We do a variety of things. Some of our groups "improv" well. Others hide behind the curtains when it's suggested. Some suggestions:
When doing improv, it works better for us in later weeks of the rotation when most of the children already have some understanding of the story. We have also found that starting out with "acting class" where children practice gestures, falling safely, expressions, etc. helps loosen everyone up so that they are more willing to put themselves out there and perhaps look foolish. (Yes, we only have 45 minutes, too.)
If using a script, make sure it is in simple language and short. A teacher or shepherd can play the role with the most lines, or most difficult lines, in groups with younger children. Whenever possible have a part with only one or two simple lines so that children who are less skilled with reading can be part of the play. By keeping the script short, you can run through it multiple times, with learning increasing each time.
For the youngest age group (K-1) we will tape a script, or have an adult read the script while the children focus on the actions, and perhaps say an occasional prompted line. We also sometimes simply read the Bible story with the children going through the actions.
The most important thing that we have done is when we started rotation, we looked at a survey that was done (somewhere on this site) which said that drama was the most difficult rotation for many churches to teach. So we asked our very best, most talented teacher, to be our regular drama rotation teacher. She is an elementary teacher, and is very good at thinking on her feet if things don't seem to be going as anticipated.
Finally, we always strive to mix it up. A script one time, improv the next. Actual retelling of the Bible story, followed by modern situation reflecting the Biblical truth. [We tried the news format, but unfortunately our kids had no knowledge of the evening news genre!!

No joke!!] This way, if there's one group that struggles with a certain format, they don't have it every time!
Look in
Drama Workshop for more ideas of ways to do drama.
Our kids love drama, but it is a challenge!
Peace,
Lisa