Salam Alaikom,
I just got back a week ago...I went to Umra by car and no letters are needed whatsoever.
All you need to carry with you is the following:
1-Valid Passport with a valid Umra visa from saudi embassy (there is a special visa for umra by car)

2-Exit permit from your employer

3-NO letter is needed from your bank nor from your employer

4-Make sure your car registration is with you and is valid...also you can check online if you have any traffic tickets...make sure you pay them before you go, check out this website www.moi.gov.qa

Good luck to you and don't forget to pray for all muslims