checking or betting here?

holdem 1/2$ i am button

utg calls, me raise, sb folds bb calls, utg calls

flop: 9sTcTh

bb checks, utg checks, me bet, bb calls, utg folds

turn: Td

bb checks, me bet

river 4h

bb bets, me calls

bb shows 66

me mucks KhQh

The question is my turn bet as i see that calling in the river is out of question: is a very bad play

Is it better to simply check the turn having possibly 6 outs OR is better in this situation bets the turn hoping for a free showdown because winning with only overdcards is a possibility?