Best results are with woody cuttings 2-3 inches long, which have some green growth. New shoots from the leaf nodes (axils) in the fall also work well. If the stems are too green, they will probably wilt. Even wilted cuttings could recover and grow eventually. Soaking the cuttings in water before planting is usually not a good idea, since this causes wilting later for many (but not all) varieties. Do not enclose planting in plastic bag. Keep cuttings shaded. (The way that cuttings respond to soaking or humidity may vary depending on temperature and time of year.) Light and warmth are needed for rooting, which takes 6-12 weeks. It takes 8-10 months to grow a full established plant from a cutting. Roots form at the axils (junction of branch to main stem). Unplanted cuttings may be temporarily transported in a plastic bag, or large softdrink cup with lid, with a wet paper towel inside (do not place the cuttings in water).
Layering has also been tried and was successful with m. flemingii. It should work with all bush mimulus, but generally is not necessary. Some propagators use mist propagation for bush mimulus cuttings, and/or grow them in a humid greenhouse. I think this is incorrect. I have observed time and again that bush mimulus do not like high humidity, which is also an invitation to mold and fungus. (A lathhouse should be ideal, although I haven't personally tried this.) If bush mimulus are grown in humid conditions, they must be gradually hardened off to become accustomed to normal lower humidity. A sudden change from high moisture or high humidity to low moisture or low humidity may cause wilting.
[updated 4/21/2001]