Now the champion from Montreal wants to unify the light heavyweight titles in a showdown with Russian Sergey Kovalev that could be one of the top fights of the year.
"That's where I've come to in my career," said Stevenson (26-1), a power puncher who put Bika (32-7-3) on the canvas in the sixth and ninth rounds but couldn't knock out the veteran from Australia before 4,729 fans at the Pepsi Colisee.
It was a fifth defence of the title Stevenson won with a first round knockout of Chad Dawson in 2013. And it was a 13th win in a row since his only defeat in 2010 against Darnell Boone, who he later knocked out in a rematch.
"I said I was ready to go 12 rounds," said Stevenson, who needed three stitches to close a cut from a head butt in the 12th. "He's tough. He's an old pro.
"I went 12 rounds when people said I could never do it."
It was a second straight defeat for Bika, who lost his WBA super-middleweight title in his last outing to American Anthony Dirrell. Bika moved up one weight class to light heavyweight to face Stevenson.
"He's a good boxer," said Bika, who still has never been stopped before the limit in his career. "He's the champion and he deserved the win."
Scores from the ringside judges were 116-110, 115-111 and 115-110, all for Stevenson.
"We said Bika would be a difficult opponent for Adonis," said promoter Yvon Michel. "Bika is very strong and has a superb chin."
The victory sets the table for a showdown, perhaps later this year, between Stevenson and Kovalev, who holds the WBA, WBO and IBF light heavyweight belts.
After four close rounds, Stevenson dominated the fifth and had Bika down in the sixth, although it appeared to be from a slip. While the Cameroon-born Aussie rebounded, the southpaw Stevenson dropped him on his backside with a short, stiff left in the ninth.
In the co-feature, rising light heavyweight prospect Artur Beterbiev (8-0), a Russian based in Montreal, knocked out former WBA champion Gabriel Campillo (25-7-1) of Spain with a crushing right uppercut in the fourth round. With the win, Beterbiev is to take over the No. 2 ranking in the IBF.