1) Think you girlfiend will find it impossible to get a visa as a single female. Only option of travelling separate would be for her to miss Saudi altogether. Maybe fly from Jordan to Sudan.
2) Sudan has problems in the news due to southern politicans being arrested and protests in response to this. May calm down quickly or could become something. Khartoum and the east used to be okay even when there was trouble in the south so may not be a problem.
3)Alternative would be to transit Saudi into Yemen then cross to Eritrea or Djibouti. Met a Czech couple in Ethiopia who had done this and said no problem. However Saudis in news for fighting rebels on Yemeni / Saudi border so don't know how easy to cross.
4) Think you will find it much much easier to get a visa in a local country than trying to source in Europe.
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