If you travel in the early morning & late in the afternoon/night, private car is your best option. Price just from 86-95$/way/4 or 7 seats private car. A good driver + no bad traffic (eg. departing city early in the morning) would take you from HCMC center to Mui Ne in less than 3.5 hours. The comfort and peace of mind are priceless.
If you go with good driver, he will know all the short cuts, and it was a very interesting trip as he took all the shortcuts through side streets. Good travel agents have many good drivers. The scenery from the car is very beautiful and you will a short stop halfway for toilet and food break.
What you need to take into account is that the car gives you the flexibility and airport pickup if you depart from Ho Chi minh airport, but it is not very much quicker than the Coach. It all depends on the traffic getting out of Saigon. It can be as short as four hours or as long as six.
You can book private car rental from Ho Chi Minh center/ airport to Mui Ne with Yourlocalbooking.com. Price: 105 USD/ 4 seat car. Book 2 ways, get 5% discount!