+1 for eMovers - I used them for a car + furnishings from UAE to Qatar. At tht time they were not established in Qatar so they sub-contracted the port clearance etc but it still worked out well. Shipped in a container.
The flat-bed suggestion is probably the most practical for a car only. Let someone else take all the pain of paperwork, queues, hassles etc. Just throw money at the problem.
The problem with driving from BAH is that there's a bit of Saudi in the way. It can be done but the paperwork is pretty horrible and there are other strange rules. For example, I believe bi-zenon headlamps are illegal in KSA and if Customs find them, they smash them - with a hammer.... might not be true, but could be.