Physical　intelligence　for　aerial　robots　greatly　enhances　grasping　and　perching　performance,　but　remains　in　emerging　stages.　This　letter　proposes　a　novel　bistable　soft　gripper　for　aerial　robots　with　high　response　speed　(0.11　s),　large　holding　force　(23.47　N),　and　active/passive　adaptive　grasping　and　perching.　The　soft　gripper　is　constructed　by　four　bistable　fingers,　tension　nets,　and　a　bidirectional　actuation　system.　The　soft　finger　evolves　from　a　simple　bistable　rotational　joint.　Tension　nets　inspired　by　spider　webs　are　proposed　to　improve　the　energy　barrier　and　grasping　performance.　Experiments　are　conducted　to　measure　the　gripper＇s　potential　energy　variation　and　grasping　performance.　One　peak　and　two　local　minima　in　the　energy　curve　indicate　the　gripper＇s　bistability.　Experimental　results　show　that　tension　nets　can　enhance　the　gripper＇s　energy　barrier,　response　speed,　and　maximum　holding　force　by　915.07%,　38.55%,　and　62.08%,　respectively.　The　gripper＇s　adjustability　of　the　energy　barrier　is　validated,　enabling　it　to　switch　active/passive　modes　as　needed.　The　experiments　demonstrated　static/dynamic　grasping　and　perching　for　various　daily　objects　with　different　shapes,　sizes,　and　stiffness　for　the　gripper　and　aerial　robot.　Finally,　the　robot　can　transport　objects　outdoors,　and　can　be　aerially　manipulated　by　external　force,　demonstrating　its　great　potential　in　aerial　application.