Axially adjacent annular booster bleed aft and forward plenums with annular common wall therebetween extend radially outwardly from transition duct. Variable bleed valve includes bleed valve door in bleed inlet in transition duct, attached to rotatable valve body rotatable about axis of rotation, operable to open and close bleed inlet to aft plenum. Rotatable plenum door clocked or circumferentially spaced apart from variable bleed valve door and attached to rotatable valve body, operable to close and open up and control flow through an inter plenum aperture in common wall. Aft and forward bleed exhaust ducts extend from booster bleed aft and forward plenums to bypass flow path. One or more heat exchanger, such as from thermal management system, may be disposed in the bleed exhaust ducts. Heat exchangers may be used for cooling oil for power gear box and/or engine bearings, air conditioning, or variable frequency generator.