Is bleaching possible if I have composite veneers?

Composites (whether fillings or veneers), are color stable.  Meaning, no amount of bleaching will improve the shade.  At high enough concentration, the composite will break down from the whitening gel.  So instead of improving esthetics, you would be destroying the restorations.  If OTHER teeth can be bleached, then bleach THEM, but avoid the veneers.

Tooth whitening materials can harm bonding if used too frequently or at high concentrations. The bonding material will not whiten. Only tooth enamel can whiten. Whiten only teeth that have not been bonded. If you are picking up stains which is common with bonding then have your dentist smooth and repolish your bonding. This is the best choice to brighten your bonding.

Bleaching composite veneers or fillings is OK especially if you are having stain on the filling material.  Your dentist may need to re-polish or re-seal the composites using a composite sealer afterwards if surface roughening is noticed.  If you are noticing stains around the edges of your composite veneers, they may need to be replaced/repaired as they will usually re-stain quickly due to a breakdown in the bond to tooth. Composite veneers have a general lifespan of 3-5 years and need more polishing maintenance over that time depending on your diet/consumption of acids etc.  Frequent brushing throughout the day and not sipping anything but water is your best preventative to re-staining.  Maybe an occasional tough up tooth whitening once per 3 months as a home gel can help too!