Standard play with bottom pair?

[checkmate36]

PokerStars 0.10/0.20 Hold'em (10 handed) FTR converter on zerodivide.cx

Preflop: Hero is Button with A[img]/images/graemlins/spade.gif[/img], 3[img]/images/graemlins/spade.gif[/img]. UTG+2 posts a blind of $0.10.

6 players see a flop of T34r with one spade. (6.5SB)

All check to hero who bets. (I think not betting is wrong) All fold except the early position player. My bet gets it heads up so I think thats a small victory already.

Turn is the 5d (4.25 BB)

EP checks, hero bets, EP folds [img]/images/graemlins/smile.gif[/img]

I usually fold bottom pair but with the Ace kicker and backdoor flush draw and nobody shows they like the hand I stayed with it. Thanks for any thoughts.