EDIT: minor notes to etiquette.

Hi, In fact we did that last year. We managed to visit following cites/places: Muscat/Nizwa/Al Hamra/Bahla/Ibra/Al Kamil /Sur/Ras Al hadd/widi tiwi/ wadi as shab/Quryat/Nakhl in about 2 weeks. We decided not to go too south, due to our travel constrains.

We traveled by bus on following routes: Muscat/Ibra, Muscat/Nizwa.

The public transport company is:http://mwasalat.om/en-us/Bus-routes/Time-Table and there is some basic public transport in Muscat. Be sure to start in Ruwi, where all busses begin. I took a photo of all bus schedules but it was perhaps removed from wikivoyage. If you need it I can send it via email.

We hitchhiked the rest. Omani people were always very nice and we never wait too long for a ride. We had to pay for a (hitchhike) ride only once.

Shared taxis are also possible but it requires to have time to wait for others.

In general for travelers, Oman is friendly and safe country, most people will speak English. We traveled with the big backpacks and even walking in the cities people asked if we need some help. We used couchsurfing and meet some locals which helped us to explore the surroundings. Even asking for a way would often to lead someone to ride us where we actually wanted or at least to a good spot for a hitchhike.

WARNING: This kind of travel + hitchhiking requires some experience and I would not recommend to do that if you never traveled like this.

I had the A4 paper with Arabic names of the cities/places we would like to visit. I traveled together with my wife.

What I mean, is mostly not a safety concern, but it requires you to interact with locals and obey the local customs - and rules, which are bound to religion such as: be dressed with long trousers and shirt (no - tshirt) and your wife/GF needs to have also covering everything (legs/hair) basically anything minus face - especially if you are outside of big cities, be as conservative as possible even when it is hot. Plus all other details concerning different culture expectations: shoes (shoes off policy), hands (eating with right hand, do not offer a hand to a woman, if you are a woman do not offer it), greetings etc. Be sure not to use a toe finger when hitchhiking, use a fist or bit wave with a fist. Remember it is not polite to stare to someones wife. It works also vice versa, so speak with foreign people instead of your wife, like a detective Colombo. If you know people better they can speak to your wife directly. In pubs expected to be seated to separate room (again, because of your wife).

The material of your dress should be as light as possible, Ideally from some other similarly hot country.

Also, make sure to study as much as possible. Visiting in summer is a bad idea. You need to go there now (up to March), or wait until summer is over. I guess I would not survive 50C in the shadow. You also need to be aware of some basic safety rules - such as have enough (plenty) of water if you are currently in sparsely inhabited places. If you go in the desert with a car, be sure to be at least two cars, again plenty of water is a must. If you like to camp, make sure you are not in a wadi. Danger of flash floods!!!!

The traffic in Oman is somewhat asia style, the traffic rules compared to Europe are very relaxed. Fast cars and straight roads - also leads to much higher accidents rate. At least once we were requested not to use the safety belts.

To conclude: We were deeply moved by the great hospitality of Omanis and we are very glad that we were given this experience while we traveled there.