ace rag in SB

approaching the mid stages of a tourney last night I'm in the SB and get dealt ace-5o, the blinds are 6-1200. UTG flat calls and it gets folded around to me. My stack is 30000 the UTG is similar the BB is less at around 10000. I call and the BB checks, the flop comes ace, 3,8 or something similar no draws.
I'll tell you my initial thinking and play and then let more experienced members have a go as I don't usually play ace rag unless on the button, but in the SB with no raisers its obligatory. Anyway I bet out 3000, I felt it was a good sum to a) chase out the others and b)to see if I was up against a bigger ace, the BB folded and the UTG after a while called. The next card was non-descript, I checked, UTG checked, the river brought another card lowish, that did not make any obvious draws or flushes. What would be the correct play here or did I make a mistake during the action up until this point? The only other way I could think is to check the flop and call and try to keep the pot small, it's just that ace-rag is so hard to play especially OOP. I'll let you all know what I did after i've had some replys. Thanks everyone I really appreciate your help...the sniper, as a postscript I'm getting better at this game thanks to all your help as I recently came in the top 50 in 5000 $4.40 freezeout and have cashed quite well in live tournaments, locally. When I win a big live tourney WPT I'll dedicate it to the cardschat community!

Ok I am noobish but since you have definite top pair and there are no draws apparent I would just continue the betting you did on the flop. Bet 3000 again on turn, maybe 6000 on river. Chances are you are not up against another ace.

Since you both as it was checked on turn, I would still bet on the river.

Without knowing the player you were up against, I probably would have checked the river with this hand because it is not a stong hand. Moreover, I am not sure I have the best hand here because he may have a higher kicker. Additionally, I am not sure I want him calling me or if I can get him fold if I bet.

thanks guys for the response, here's what I did, bet 6000 on the river a)because he checked the turn and b)because i felt it was the only way to win the hand as if he called I still had top pair and c)I still had 20000 left to play with. As it was he called and showed ace-6o and his kicker beat mine, I'm still doubtful as to his pre-flop call in EP with such a marginal hand but that's the way it goes