The `Single Ladies` singer has been going out on morning drives in New York with her 40-year-old husband, avoiding the rush hour glare of commuters and steering clear of paparazzi.
A source said: "Jay and Beyonce normally go out mid-morning when it`s quiet. Their bodyguards are always in tow but they never ride in the car with them."
Beyonce, 28, is doing so well in the lessons that Jay-Z, 40, is looking to buy a car for her - although she is keen to avoid anything too flashy, scuppering his plans to get her a Bentley.
The source added to The Sun newspaper: "Beyonce wants something smaller. Money isn`t an issue but she doesn`t want to feel like she`s driving a tank.
"She does want a car that`s big enough to take out her family and friends if she needs to though."
Beyonce has previously revealed she would like to start a family at some point in the future, and wants to be just like her own mother Tina - who helped nurture her talent in Destiny`s Child as a young girl.
She said: "It`s not time for that yet. But definitely there will be a time. I want to be a great mother, the kind of mother that I have. I want the same bond that I had with my mom and that would be enough for me.
"The security and love I feel being in a relationship, a marriage, it`s absolutely incredible. Incredible."
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