Four to Broadway on turn

An interesting hand came up. The turn brought a fourth broadway card. JQKT with two to a flush. I was in early position with AJ in my hand but did not have any of the flush suit. 3 players were behind me. The flop was checked around.

Because I had no redraw and was in early position, I did not want the pot to get big. I also felt it was likely that somebody else had broadway as all they needed was an Ace with any of T-K. I checked and to my surprise it was checked around again. The river brought the flush and I check/folded.

I guess my question is, my turn play was check/call, but should it have been bet/call:fold, only folding to a substantial re-raise. Something like, one caller, and then a pot raise.