Turning AK into a bluff

I still struggle in spots like this, especially when deciding to turn a missed AK into a bluff. In the hands before, I made two highly polarized river overbets with the nuts and wanted to balance my range. Is this generally the right way to think about it?

To be honest, the concept of which range I arrive at the river with and then choosing the correct part of that range to place an indifferent river overbet as a bluff feels a bit too advanced for me right now. Maybe someone can help me understand how to approach and navigate these spots in a more simplfied approach. Thanks in advance.

GGPoker, Hold'em No Limit - $0.10/$0.25 - 6 players
Replay this hand on Pokeit

UTG (Hero): $30.77 (123 bb)
MP: $62.26 (249 bb)
CO: $3.83 (15 bb)
BU: $46.52 (186 bb)
SB: $26.50 (106 bb)
BB: $30.89 (124 bb)

Pre-Flop: ($0.35) Hero is UTG with K♠ A♣
Hero raises to $0.50, MP 3-bets to $1.52, 2 players fold, SB calls $1.42, 1 fold, Hero 4-bets to $6, 1 fold, SB calls $4.48

Flop: ($13.77) 9♣ 3♠ 2♦ (2 players)
SB checks, Hero bets $4.55, SB calls $4.55

Turn: ($22.87) 8♥ (2 players)
SB checks, Hero bets $20.22 (all-in), SB calls $15.95 (all-in)

River: ($54.77) 5♠ (2 players, 2 all-in)

Total pot: $54.77 (Rake: $2.25)

Showdown:
UTG (Hero) shows K♠ A♣ (high card, Ace)
(Equity - Pre-Flop: 30%, Flop: 14%, Turn: 7%, River: 0%)

SB shows K♥ K♣ (a pair of Kings)
(Equity - Pre-Flop: 70%, Flop: 86%, Turn: 93%, River: 100%)

SB wins $52.52