EXCLUSIVE

"Little Women: Atlanta" star Ashley "Minnie" Ross says she had just 1 beer when she got busted for DUI.

According to a police report obtained by TMZ ... cops in Chattanooga, Tennessee were notified Thursday just before 3 AM of a female slumped over in the driver's seat of an SUV. When cops responded, they woke up the 4'3'' reality star and immediately smelled booze on her breath.

When asked if she had any drinks earlier that night, cops say Minnie told them she had just 1 beer. She was instructed to get outta the car and given a series of field sobriety tests, which she bombed ... swaying and using her arm for balance.

She was asked to recite the alphabet from letter E and stop at W ... but Minnie stopped at Z. She was asked to count backward from 69 and stop at 39 but she stopped at 1.

Despite the very detailed police report ... a source close to Minnie says she passed all of the field sobriety tests and she was texting -- not asleep at the wheel -- when cops showed up.