Smith was making his second appearance in the division since his reign as WBA super-middleweight champion ended at the hands of Saul Alvarez in December 2020 - his only defeat in 30 fights.
An action packed four rounds saw Bauderlique go down twice in the fourth, with a devastating left hook prompting referee Hector Afu to immediately wave off the fight.
"Good performance. He engaged and caught me a few times," said Liverpool's Smith as he looks to become a two-weight world champion.
"I'm happy with the finish and we move in. It was a good shot and it's a shot I'm comfortable throwing.
"I just want to keep winning and at some point I'll become a world champion."
Olympic silver medallist Ben Whittaker produced a dominant victory over his former amateur opponent Petar Nosic.
Whittaker, a member of Team GB at Tokyo 2020, was never in trouble against the Croatian in a successful second professional outing.
It took just 76 seconds for Ramla Ali to polish off Crystal Garcia Nova with an overhand right that sent the underdog's gum shield flying out of her mouth.
The fight was the first women's bout to be staged in Saudi Arabia and British-based Somali Ali impressed on her seventh outing, with promoter Eddie Hearn promising a world title fight next year.
"I'm looking forward to having a little break now because my last two fights I have been fighting and training with a fractured wrist and toe," Ali said.
"But this was a massive opportunity and I couldn't say no even though I have been in a world of pain."