i have been there about 11 times in my 25 years stay in Doha, but i always traveled by my car all the way, i used to enjoy long drive and there is big difference in total expence too.

abu samra border is about 95km (1 hour drive)
bodrer clearance depends, on weekends it takes more than one hour to clear from both immigrations (once it took more than 2hours for us to clear)Thu. morning is working day, hopefully you will clear within 1 hr.

from Salwa border to Hafouf city is about 150 km (1hr and 45min. drive)
it needs another half an hour or 45 min. to get out of the city(Hafouf) for Dammam road, because you are new there

from hafouf to Dammam is about 300km (3.5 hrs)
i think you need to reach airport two hours in addvance.
for first time in a city takes more time than known person to find a way.
calculate now and add some safe time too.
by the way which car you have?

above all when we were travelling first time (1983) we were very nerves, some one said to my father and i still remember those words he said "ON THIS JURNEY YOU WILL FEEL THAT SOME ONE IS HELPING YOU".

after clearing from saudia immigration there is Saudia Insurance company office within the permises (100/=SR)

there is lot more to write and lot more to speak on this
if you have time and wish you can call me on 4950457 up to 3:00 pm or 5327457 at any time, i always feel very spirtual while sharing information about this.......
any way all the best, drive carefully and don't forget to pray for every muslim