Mustafa began and spent all of his career to date with Al-Ahli. He played for the Al-Ahli academy junior and youth teams. Bassas plays in more than one position: right back, central midfielder, attacking midfielder, winger, and second striker. He is known for his pace, shot power, and leadership skills . Czech coach Karel Jarolím gave him his debut in the Al-Ahli first team.
In the 2012 AFC Champions League, Bassas played in his first rivalry match in Jeddah against Ittihad, proving to be best player on the pitch, showing a lot of skill and talent when on the ball even though his side lost the first leg 1-0. The second leg however was won by Al-Ahli 2-0, with Bassas producing a man of the match display with an assist to Victor Simões, who also scored the second goal in the 83rd minute and to help the team qualify to the final against eventual winners Ulsan Hyundai. Al-Bassas helped Al-Ahli in obtaining Saudi Federation Cup 2012-13. Al-Ahli fans chose Al-Bassas as Player of the Season in 2012-13.
In 2013, Al-Bassas is featured, alongside Lionel Messi, on the official cover of the video game FIFA 14 as distributed for the Middle East for all platforms except the Wii and Nintendo 3DS versions. He did not appear on the PlayStation 4 and Xbox One versions of the game either, although those versions featured a revised cover.