Bastiansen was a regular member of the Denmark Davis Cup team throughout the 1980s, which included stints in the World Group.

He helped Denmark qualify for the World Group for the first time when he won both of his singles rubbers in the 1982 Europe Zone final against Hungary in Budapest.

[1] He was a member of the Danish team that defeated Spain in the 1988 Davis Cup World Group, to make the quarter-finals.

[1] In 1983 he had a win over former world number one Ilie Năstase at a Grand Prix tournament in Viña del Mar.

[5] He played in one Grand Slam event, the men's doubles at the 1987 French Open, partnering Michael Tauson.