There are several tour companies in Saigon willing to help you with this. You can arrange for such trip ahead of time by contacting them over the phone (from where you are now), or you can arrange the trip when you are there, via your hotels' concierge.
The cost depends on how many days you plan to stay in Kontum, as it is likely that the driver will stay there with you (instead of driving back to Saigon.) My estimate is something like this:
$50-$100 per person round-trip (for the bus) + $15 per day for the driver to stay there + tip (e.g. $50 - $100 for a one-week stay)