Villain is 59/0/1 over 17 hands.

First, I have the nuts with no redraw. Should I just try to get to showdown cheap and fold if a bad card comes?

Second, once the action on the flop and turn goes the way it does, it seems this is a great opportunity to bluff. It looks like I could possibly fold off another JT. It looks like at worst I'm splitting so what size bet would be worth it to try to win half the pot?

Full Tilt Poker $0.25/$0.50 Pot Limit Omaha Hi - 4 players
The Official 2+2 Hand Converter Powered By DeucesCracked.com

Hero (BB): $49.25
CO: $56.75
BTN: $43.45
SB: $130.35

Pre Flop: ($0.75) Hero is BB with 9 J T 5
CO calls $0.50, 2 folds, Hero checks

Flop: ($1.25) 9 8 7 (2 players)
Hero checks, CO bets $1.25, Hero raises to $5, CO raises to $10.60, Hero calls $5.60

Turn: ($22.45) 7 (2 players)
Hero checks, CO checks

River: ($22.45) 2 (2 players)
Hero

I think he has exactly JT and u should have fired the turn if you're just gonna call the flop

I can't understand why you flatted the flop. If he has QJT then that sucks but he also has lower straights and top set etc in his range. If there was a flushdraw on the flop then I'd be more inclined to flat.

You think a player this passive really 3-bets a c/r with anything other than JT? Maybe a set but I think that has to be discounted. What is the point of pushing here? Most of the time I'm splitting or getting freerolled right?

I like that line. A bet fold on the turn there looks pretty good in retrospect.

Yeah I do actually. I play HUPLO and normally play aggressive. Very passive villains will spazz out from time to time and reraise w/ non-nut made hands since I "cant have anything since I'm betting every street". And from my experience, if villain has a non-nut straight or a set he's calling a potsized reraise the majority of the time.
This is dependent on your own image tho.