Hi Expat,
We are using 2 companies:
1. Heli Air Monaco: the scheduled shuttle is the one most used by our customers. The advantage is that they bring you wherever you live in Monaco and pick you also up from wherever it needs to be. They are even cheaper than limousine transfer.
2. For the "I do not want to share a chopper customer", There is Monacair. Quite steep prices, they operate a gorgeous Agusta 109. They fly for the Prince.
Hope this helps, looking forward to Nice 2014!