In my own mediation practice, I billed on an hourly basis for
the actual mediation sessions (which, in my opinion, could not and should not be fairly estimated in advance — except to give a likely range), but used a flat fee for drafting the resultant memorandum of understanding.
In addition, most mediators spend a fair amount of time outside of
actual mediation sessions in phone calls or email correspondence with the parties, or in research, writing summary memos and drafting agreements.