Linear global stability analysis is performed on a laminar separation bubble formed due to surface waviness. The eigenspectrum shows a globally unstable mode, responsible for the three-dimensionalisation of the bubble, and a family of low-frequency globally stable modes. An adjoint sensitivity analysis shows high sensitivity of the stable modes upstream of the bubble’s reattachment point. Direct numerical simulation (DNS) alongside with a linear impulse response analysis are performed. DNS shows that, when transition occurs due to self-excited mechanisms, low-frequency upstream propagating waves form inside the bubble; this is not the case in linear impulse analysis. It is conjectured that these upstream propagating waves correspond to the low-frequency stable modes in the spectrum which become active through nonlinearity when transition occurs.