The 25-year-old, who recently returned to fitness following a cruciate knee ligament operation, has joined the Robins until January 16 following a successful trial at Ashton Gate.
"He's proved his fitness and is a quality addition to our squad," said manager Derek McInnes. "He's had a poor time with injuries but has demonstrated the strength to come back on each occasion.
"We were more than happy to take a look at somebody with his quality and he has shown his fitness, including playing in a practice match in the week.
"He offers us a good option and is a good person too. It's a low-risk deal until mid-January, which gives him the opportunity to stake a claim for an extended stay if all goes well."
Bates was capped by England at Under-18 and Under-19 levels.