Leeds went ahead in the seventh minute when a lovely move down the left ended with Junior Firpo's cross being headed home by Bamford into the far corner.
Betis equalised just three minutes later when Aitor's shot from inside the box trickled past Illan Meslier and hit the post before finding the back of the net.
Leeds squandered a golden chance to go back ahead moments later when Jack Harrison blazed over from inside the box.
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After a decent build up down the right, Raphinha's firm low drive was then kept out by a strong save from Rui Silva.
But Betis went ahead in the 23rd minute when Leeds were caught out down the left flank and a cross set up Borja Iglesias who fired home from the middle of the box.
After seemingly injuring himself in the build up to the goal, Diego Llorente was then taken off and replaced by Jamie Shackleton who moved to right back as Luke Ayling moved into the heart of the defence.
Leeds then nearly fell two goals behind as Rodri cut inside from the right and curled a shot just wide. The same player then blazed over after winning the ball in the middle of the park.
Betis were causing plenty of bother but Leeds were then denied an equaliser as Rodrigo's effort from the middle of the box was cleared off the line from a move that began with a fine challenge from Shackleton in defence.
Rodrigo again went close in the 39th minute when heading wide from a Raphinha free-kick.
Back came Betis and a fierce long range effort from Nabil Fekir was eventually gathered by Meslier at the second attempt as the last act of the half.
Whites head coach Marcelo Bielsa made a double change during the break as Tyler Roberts and Mateusz Klich replaced Bamford and Junior Firpo.
Dallas moved to left back as a result.
Klich saw an effort from the edge of the box saved six minutes after the restart but Betis opened up a two-goal cushion in the 55th minute when a cross from Sabaly was parried into the net by Meslier.
Leeds immediately responded and pulled a goal back through a cool finish from Klich who found himself free in the area after Betis lost the ball.
Betis remained a threat and Fekir sent a powerful drive just wide.
At the other end, Rodrigo was then played in behind the defence but opted for a square ball instead of shooting and Betis cleared.
A cross from Costa then almost led to a spectacular own goal as a clearance flew over the bar but back came Betis with Fekir firing just wide.
Fekir then needlessly kicked out at Struijk who was taken off soon afterwards.
Both sides then had chances to bag the game's sixth goal and Meslier saved well to deny Camarasa before Roberts curled an effort well wide at the other end.
Leeds then had one last opportunity as Costa found himself free and the winger eventually played in Rodrigo whose shot was blocked.
Leeds United v Real Betis: Meslier, Ayling, Koch, Llorente (Shackleton 24), Firpo (Klich 45), Struijk (Greenwood 84), Dallas, Raphinha, Harrison (Costa 65), Rodrigo, Bamford (Roberts 45). Subs not used: Caprile.
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Thank you Laura Collins