Certainly bike commuting avoids the being stuck in traffic stress but it comes with other stresses like being on an exposed vehicle dealing with aggressive nutcases, or people gliding over into the space you are occupying while yakking on their cell phone not signalling or looking.

I find it much less stressful overall than driving to work or riding public transit. But I know someone else that tried bike commuting only to find it increased her stress level too much and she quit.