hi there,
you can ask your relatives to get the visa for you from saudi, but that will be too expensive, 100 riyals to get the visa, and to stamp the same visa in doha costs you around 450 qr, (agent charges, as saudi embassy do not entertain general public)
so the best way i suggest is to take a transit visa by road for saudi(from registered agents, qr 125) as if you are travelling to bahrain, once you enter saudi you can stay there for 3 days, before the third day make an exit to bahrain (visa fee 10 BD) take a ride is bahrain for about an hour and re enter saudi with same transit visa and if you want you can stay another 3 days in saudi, then come back to doha,
ps-it it compulsory to make an exit from saudi to the country which you have mentioned while taking a transit visa
hope this will help you