Question
Can you take a snip from an outdoor gardenia bush & start a plant from that?

Answer
Gene,

If you take 20 cuttings you might have 2 root.

I would try air layering it. I have cut one off and the top nor the bottom survived. If your try air layering it you have at least a 50-50 chance that it will survive. I would do it outside in a shady location and keep the plant on the dry side while you are air layering it.  You can get instructions for air layering at the following sites.

http://aggie-horticulture.tamu.edu/earthkind/landscape/air-layering/

http://www.instructables.com/id/Propagating-Plants-by-Air-Layering/

http://www.learn2grow.com/gardeningguides/propagation/techniques/LearnHowToAirLa

Good luck!

Darlene