"I probably haven't bowled as well as I could have done, and probably got away with one or two, but that's cricket," Bess told reporters after the day's play.
The former world No.1 is reportedly in good health and isolating at his residence in Surrey.
The three-time Major champion had been due to fly down to Australia this week to complete a two-week quarantine Down Under before the first Grand Slam of the season on February 8.
Spin was introduced in the 11th over and Dom Bess with his second ball accounted for the wicket of Kusal Perera for 20 when the batsman top edged a reverse sweep to England captain Joe Root at first slip.
The Thailand Open is the first of three consecutive tournaments played in strict bio-secure conditions and behind closed doors in Bangkok, culminating in the World Tour Finals from January 27.
Sociedad, who made a blistering start to the La Liga season but have since faded, ran their hearts out to keep Barca at bay in a tight match before the game opened up in extra time, when both sides came close to finding a winner.
It was not a vintage performance for Spurs defenders Davinson Sanchez and Eric Dier who were both beaten in the air by Cavaleiro for Fulham's goal. Mourinho did not name names but pointed the finger at "individual" mistakes.