There is a regular bus service between Muscat and Dubai (UAE). There are private operators as well as state owned Oman National Transport Company (ONTC) and the ride (which usually takes between 4 to 5 hours) is quite comfortable, thanks to the excellent roads.
ONTC Oman national transport company operates Dubai - Muscat and Dubai - Salalah. The bus to Muscat departs from Al rigga road in Deira, Dubai at 7.15 am and in the afternoon. The bus to Salalah departs 3 pm from the same bus sation. The tickes are bought at Al Manhal stationary by the bus stop and costs 55 dirham one way to Muscat(dec 2010). The bus stop is hard to find, it is close to the Caravan restaurant and close to the Dnata building, the taxi drivers know where the bus stop is. To go to Nizwa you need to go with the Salalah bus. Dress warm for the bus ride and prepare for border control including bagage check! If you enter UAE through Dubai you dont need to pay for Visa for Oman, show your stamp at the border control.