Extra short handed with AT

This hand impacted some later hands so I keep coming back to it. I don't know that it's a particularly unique situation, but I'm looking to learn so I'm trying to find any hands worth posting. Thanks!

Absolute Poker No-Limit Hold'em, $0.10 BB (4 handed) Absolute-Poker Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

BB ($4.75)
Hero ($18.04)
Button ($11.70)
SB ($3.60)

Preflop: Hero is UTG with A, T.
Hero raises to $0.3, Button calls $0.30, 1 fold, BB calls $0.20.

Flop: ($0.95) 5, 4, 6 (3 players)
BB checks, Hero bets $1, Button folds, BB calls $1.

Turn: ($2.95) K (2 players)
BB checks, Hero bets $3, BB calls $3.

River: ($8.95) 8 (2 players)
BB bets 0.45 , Hero calls $0.45.

Final Pot: $9.40

Results in white below:
BB has Jh 7s (straight, eight high).
Hero has Ac Ts (high card, ace).
Outcome: BB wins $9.40.

Got reads?

I think this is total spew, but the depth of your sin depends on your opponents.

Turn spew is the worst part. This little stack isn't folding anything - pair, draw, queen-high - for his last $3.50 when he already has put in $1.50 and there's still one super-exciting card to come. Check behind and hope for your ace. If the river is a blank and he checks it again I could see maybe making a smaller bet (1.50 - 2.00) just to get him to fold truly crappy pairs.

betting any amount on flop is terrible, as played shoving turn isnt the worst thing ever since u beat draws, but dont leave him any money for the river. better yet just c/f every street.

Really? Everyone keeps saying "bet the flop, bet the flop" when you were the aggressor pre-flop. What makes this case different?

Edit: And in terms of reads, I had only seen her play a few hands. Every time she caught a piece of the flop she bet it though.