Armstrong earned three championship rings with the Chicago Bulls in the early 1990s. A superior three-point shooter with good quickness and passing skills, he was an NBA All-Star in 1994 and the first overall pick of the 1995 Expansion Draft, going to the Toronto Raptors.

He quickly was traded to Golden State for two players and the rights to three more, and spent 2 seasons with the Warriors before playing for Charlotte and Orlando Magic and finally rejoining Chicago Bulls as a veteran free agent prior to the 1999-2000 season. He announced his retirement after his 11th pro season and accepted a position in the Bulls' front office as a special assistant to Vice President of Basketball Operations Jerry Krause. 

After working with the Bulls, B.J. accepted a position working as a NBA agent.