There are regular public buses every day from Kathmandu to Arughat Bazaar that leaves early in the morning (5:50 to 8:30 AM. Obviously, public bus is more crowded and take a long time. As you are asking for a private Jeep (Scorpio/ Land cruiser 6 to eight sitters), this is the best option for a much more comfortable journey for the whole day. To hire private vehicles cost will be about 200 to 250 USD for a single way.