$25 NLHE Full Ring: River line against passive player

poker stars, $0.10/$0.25 No Limit Hold'em Cash, 7 Players

SB: $25.77 (103.1 bb)
BB: $10.03 (40.1 bb)
MP1: $25 (100 bb)
MP2: $25 (100 bb)
MP3: $38.73 (154.9 bb)
Hero (CO): $25 (100 bb)
BTN: $25.58 (102.3 bb) 20/0/1 in 29 hands, passive looking

Preflop: Hero is CO with K K
3 folds, Hero raises to $0.75, BTN calls $0.75, SB folds, BB calls $0.50

Flop: ($2.35) 4 2 9 (3 players)
BB checks, Hero bets $1.68, BTN calls $1.68, BB folds

Turn: ($5.71) 6 (2 players)
Hero bets $4.08, BTN calls $4.08

River: ($13.87) 8 (2 players)
Hero? Its possible he has a missed club draw, do we check and let him bluff his missed draws or do we bet 40-50% pot and fold to a shove. If he is so passive is he capable of bluffing?

Against a guy this passive, just bet/fold for half pot to charge his A9 type hands. He's not going to bluff his missed draws. But you had the right thought process.