No, he says he wanted to get to DS9 straight away. We never learn if he was granted that wish
Sisko says in "Doctor Bashir, I presume" that Bashir came to DS9 right out of medical school:
ZIMMERMAN: What were your initial impressions of Doctor Bashir? Good and bad.
SISKO: Young, eager, ambitious. He was fresh out of medical school, looking forward to his first taste of frontier medicine. Sometimes he let that natural impulse override his sense of decorum.