Cut the chicken breasts into thin strips. Cut the spring onions into rings and the red peppers into bite-sized pieces.
Place the chicken strips in a ziplock bag or bowl, coat lightly with some sesame oil, and refrigerate for 1 to 2 hours.
Heat the remaining sesame oil in a large pan over medium-high heat. Add the red pepper pieces and fry for 2-3 minutes until they start to soften. Remove and set aside.
Add the drained chicken strips to the pan and fry over medium-high heat for 5-7 minutes, stirring occasionally, until cooked through (internal temperature 74°C / 165°F).
Return the red peppers to the pan, add the spring onions and bamboo shoots, and cook for 2-3 minutes more until heated through.