I agree with the other posters who say that you should get some value. I think I bet $2.50, as I'm getting raised by a flush either way. With that said, there's no way Jx is folding for $4 (usually), so I wouldn't worry too much about that.
I would consider betting a bit more on the turn. Perhaps $1.35 or so. That way, a $4 bet on the end is less than pot, and is more likely to be called down that the >pot bet that it is as played.