What you do next is going to depend upon how confident you are in your skills to bring her along. Teach her how to lunge than move up to ground driving. You don't need a harness or bridle at this point You can use your saddle or a $20 web surcingle and halter. Spend the time teaching her her name and voice commands. Pick one set of terms and stick with them. Get her soft and straight in your hands. Get her solid with whoa. Do all the desentitization again (you've changed things up where the stimulation is coming from plus added a layer that she also needs to keep track of). Now you need a harness.
I would recomment picking up either Doris Ganton's "Breaking and Training the Driving Horse" or Guffey and Winkel's "The Essential Guide to Carriage Driving" even if you aren't planning on doing any of the major work breaking her to harness. Being familiar with the correct terminology will speed things up, help eliminate any confusion and help keep everyone safe. I would also look into the American Driving Society, www.americandrivingsocity.org
for a local contact that can help you.